PDE: Partial Differentiable Equation

Contributed by Chunyang Zhang.

1. Physics-informed machine learning. Nature Reviews Physics, 2021. paper

   George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.

2. Neural operator: Learning maps between function spaces. arXiv, 2021. paper

   Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

3. Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework. Physical Review Fluids, 2018. paper

   Jinlong Wu, Heng Xiao, and Eric Paterson.

4. Integrating scientific knowledge with machine learning for engineering and environmental systems. ACM Computing Surveys, 2023. paper

   Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar.

5. Physical laws meet machine intelligence: Current developments and future directions. Artificial Intelligence Review, 2022. paper

   Temoor Muther, Amirmasoud Kalantari Dahaghi, Fahad Iqbal Syed, and Vuong Van Pham.

6. A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis.

7. Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Beyond Traditional AI: The Impact of Machine Learning on Scientific Computing, 2022. book

   MingyuanYang and John T.Foster

8. When physics meets machine learning: A survey of physics-informed machine learning. arXiv, 2022. paper

   Chuizheng Meng, Sungyong Seo, Defu Cao, Sam Griesemer, and Yan Liu.

9. Physics-guided, physics-informed, and physics-encoded neural networks in scientific computing. arXiv, 2022. paper

   Salah A. Faroughi, Nikhil M. Pawar, C´elio Fernandes, Subasish Das, Nima K. Kalantari, and Seyed Kourosh Mahjour.

10. Physics-informed machine learning: A survey on problems, methods and applications. arXiv, 2022. paper

    Zhongkai Hao, Songming Liu, Yichi Zhang, Chengyang Ying, Yao Feng, Hang Su, and Jun Zhu.

11. An overview on deep learning-based approximation methods for partial differential equations. arXiv, 2020. paper

    Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, and Benno Kuckuck.

12. Three ways to solve partial differential equations with neural networks—A review. GAMM‐Mitteilungen, 2021. paper

    Jan Blechschmidt and Oliver G. Ernst.

13. Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review. GAMM‐Mitteilungen, 2021. paper

    Alexander Heinlein, Axel Klawonn, Martin Lanser, and Janine Weber.

14. Physics-guided, physics-informed, and physics-encoded neural networks in scientific computing. arXiv, 2022. paper

    Salah A Faroughi, Nikhil Pawar, Celio Fernandes, Subasish Das, Nima K. Kalantari, and Seyed Kourosh Mahjour.

15. Partial differential equations meet deep neural networks: A survey. arXiv, 2022. paper

    Shudong Huang, Wentao Feng, Chenwei Tang, and Jiancheng Lv.

16. Solving differential equations with Deep Learning: A beginner's guide. arXiv, 2023. paper

    Luis Medrano Navarro, Luis Martín Moreno, and Sergio G Rodrigo.

17. Deep learning algorithms for solving differential equations: a survey. Journal of Experimental & Theoretical Artificial Intelligence, 2023. paper

    Harender Kumara and Neha Yadav.

1. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 2020. paper

   Raissi Maziar, Alireza Yazdani, and George Em Karniadakis.

2. Deep hidden physics models: Deep learning of nonlinear partial differential equations. JMLR, 2018. paper

   Maziar Raissi.

3. A universal PINNs method for solving partial differential equations with a point source. IJCAI, 2022. paper

   Xiang Huang, Hongsheng Liu, Beiji Shi, Zidong Wang, Kang Yang, Yang Li, Min Wang, Haotian Chu, Jing Zhou, Fan Yu, Bei Hua, Bin Dong, and Lei Chen.

4. Parallel physics-informed neural networks via domain decomposition. JCP, 2021. paper

   Khemraj Shukla, Ameya D.Jagtap, and George Em Karniadakis.

5. Kolmogorov n–width and Lagrangian physics-informed neural networks: A causality-conforming manifold for convection-dominated PDEs. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Rambod Mojgani, Maciej Balajewicz, and Pedram Hassanzadeh.

6. Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   N.Sukumar and Ankit Srivastava.

7. Physics-informed multi-LSTM networks for meta-modeling of nonlinear structures. Computer Methods in Applied Mechanics and Engineering, 2020. paper

   Ruiyang Zhang, Yang Liu, and Hao Sun.

8. Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.

9. Multi-output physics-informed neural networks for forward and inverse PDE problems with uncertainties. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   MingyuanYang and John T.Foster

10. PPINN: Parareal physics-informed neural network for time-dependent PDEs. Computer Methods in Applied Mechanics and Engineering, 2020. paper

    Xuhui Meng, Zhen Li, Dongkun Zhang, and George Em Karniadakis.

11. CAN-PINN: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Pao-Hsiung Chiu, Jian Cheng Wong, Chinchun Ooi, My Ha Dao, and Yew-Soon Ong.

12. Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Thomas O’Leary-Roseberry, Umberto Villa, Peng Chen, and Omar Ghattas.

13. Physics-augmented learning: A new paradigm beyond physics-informed learning. NIPS, 2021. paper

    Ziming Liu, Yuanqi Du, Yunyue Chen, and Max Tegmark.

14. Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm. Physics Letters A, 2021. paper

    Yifan Mo, Liming Ling, and Delu Zeng.

15. Solving Benjamin–Ono equation via gradient balanced PINNs approach. The European Physical Journal Plus, 2022. paper

    Xiangyu Yang and Zhen Wang.

16. Robust learning of physics informed neural networks. arXiv, 2021. paper

    Chandrajit Bajaj, Luke McLennan, Timothy Andeen, and Avik Roy.

17. Learning physics-informed neural networks without stacked back-propagation. arXiv, 2022. paper

    Di He, Wenlei Shi, Shanda Li, Xiaotian Gao, Jia Zhang, Jiang Bian, Liwei Wang, and Tieyan Liu.

18. NeuralPDE: Automating physics-informed neural networks (PINNs) with error approximations. arXiv, 2021. paper

    Kirill Zubov, Zoe McCarthy, Yingbo Ma, Francesco Calisto, Valerio Pagliarino, Simone Azeglio, Luca Bottero, Emmanuel Luján, Valentin Sulzer, Ashutosh Bharambe, Nand Vinchhi, Kaushik Balakrishnan, Devesh Upadhyay, and Chris Rackauckas.

19. Physics informed RNN-DCT networks for time-dependent partial differential equations. ICCS, 2022. paper

    Benjamin Wu, Oliver Hennigh, Jan Kautz, Sanjay Choudhry, and Wonmin Byeon.

20. Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation. JCP, 2022. paper

    Amirhossein Arzani, Kevin W.Cassel, and Roshan M.D'Souza.

21. A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations. JCP, 2022. paper

    Lei Yuan, Yiqing Ni, Xiangyun Deng, and Shuo Hao.

22. A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Shahed Rezaei, Ali Harandi, Ahmad Moeineddin, Baixiang Xua, and Stefanie Reese.

23. Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations. Computers & Mathematics with Applications, 2023. paper

    Siping Tang, Xinlong Feng, Wei Wu, and Hui Xu.

24. A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Revanth Mattey and Susanta Ghosh.

25. RPINNs: Rectified-physics informed neural networks for solving stationary partial differential equations. Computers and Fluids, 2022. paper

    Pai Peng, Jiangong Pan, Hui Xu, and Xinlong Feng.

26. A-WPINN algorithm for the data-driven vector-soliton solutions and parameter discovery of general coupled nonlinear equations. Physica D: Nonlinear Phenomena, 2022. paper

    Shumei Qin, Min Li, Tao Xu, and Shaoqun Dong.

27. Physics-informed neural networks with adaptive localized artificial viscosity. arXiv, 2022. paper

    E.J.R. Coutinho, M. Dall'Aqua, L. McClenny, M. Zhong, U. Braga-Neto, and E. Gildin.

28. Physics-informed neural operator for learning partial differential equations. arXiv, 2021. paper

    Zongyi Li, Hongkai Zheng, Nikola Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, and Anima Anandkumar.

29. Anisotropic, sparse and interpretable physics-informed neural networks for PDEs. arXiv, 2022. paper

    Amuthan A. Ramabathiran and Prabhu Ramachandran.

30. Fast neural network based solving of partial differential equations. arXiv, 2022. paper

    Jaroslaw Rzepecki, Daniel Bates, and Chris Doran.

31. Discontinuity computing using physics-informed neural network. arXiv, 2022. paper

    Li Liu, Shengping Liu, Hui Xie, Fansheng Xiong, Tengchao Yu, Mengjuan Xiao, Lufeng Liu, and Heng Yong.

32. Learning differentiable solvers for systems with hard constraints. arXiv, 2022. paper

    Geoffrey Négiar, Michael W. Mahoney, and Aditi S. Krishnapriyan.

33. Momentum diminishes the effect of spectral bias in physics-informed neural networks. arXiv, 2022. paper

    Ghazal Farhani, Alexander Kazachek, and Boyu Wang.

34. Δ-PINNs: Physics-informed neural networks on complex geometries. arXiv, 2022. paper

    Francisco Sahli Costabal, Simone Pezzuto, and Paris Perdikaris.

35. Replacing automatic differentiation by Sobolev Cubatures fastens physics informed neural nets and strengthens their approximation power. arXiv, 2022. paper

    Juan Esteban Suarez Cardona and Michael Hecht.

36. FO-PINNs: A first-order formulation for physics informed neural networks. arXiv, 2022. paper

    Rini J. Gladstone, Mohammad A. Nabian, and Hadi Meidani.

37. Augmented physics-informed neural networks (APINNs): A gating network-based soft domain decomposition methodology. arXiv, 2022. paper

    Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, and Kenji Kawaguchi.

38. Physics-informed neural networks for operator equations with stochastic data. arXiv, 2022. paper

    Paul Escapil-Inchauspé and Gonzalo A. Ruz.

39. Physics-informed neural networks with unknown measurement noise. arXiv, 2022. paper

    Philipp Pilar and Niklas Wahlstrom.

40. On the compatibility between a neural network and a partial differential equation for physics-informed learning. arXiv, 2022. paper

    Kuangdai Leng and Jeyan Thiyagalingam.

41. Pre-training strategy for solving evolution equations based on physics-informed neural networks. arXiv, 2022. paper

    Jiawei Guo, Yanzhong Yao, Han Wang, and Tongxiang Gu.

42. L-HYDRA: Multi-head physics-informed neural networks. arXiv, 2023. paper

    Zongren Zou and George Em Karniadakis.

43. PINN for dynamical partial differential equations is not training deeper networks rather learning advection and time variance. arXiv, 2023. paper

    Siddharth Rout.

44. Wavelets based physics informed neural networks to solve non-linear differential equations. Scientific Reports, 2023. paper

    Ziya Uddin, Sai Ganga, Rishi Asthana, and Wubshet Ibrahim.

45. Improved training of physics-informed neural networks using energy-based priors: A study on electrical impedance tomography. ICLR, 2023. paper

    Akarsh Pokkunuru, Pedram Rooshenas, Thilo Strauss, Anuj Abhishek, and Taufiquar Khan.

46. Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems. arXiv, 2023. paper

    Sarah Perez, Suryanarayana Maddu, Ivo F. Sbalzarini, and Philippe Poncet.

47. Efficient physics-informed neural networks using hash encoding. arXiv, 2023. paper

    Xinquan Huang and Tariq Alkhalifah.

48. Ensemble learning for physics informed neural networks: A gradient boosting approach. arXiv, 2023. paper

    Zhiwei Fang, Sifan Wang, and Paris Perdikaris.

49. On the limitations of physics-informed deep learning: Illustrations using first order hyperbolic conservation law-based traffic flow models. arXiv, 2023. paper

    Archie J. Huang and Shaurya Agarwal.

50. Achieving high accuracy with PINNs via energy natural gradients. arXiv, 2023. paper

    Johannes Müller and Marius Zeinhofer.

51. Implicit stochastic gradient descent for training physics-informed neural networks. arXiv, 2023. paper

    Ye Li, Songcan Chen, and Shengjun Huang.

52. NSGA-PINN: A multi-objective optimization method for physics-informed neural network training. arXiv, 2023. paper

    Binghang Lu, Christian B. Moya, and Guang Lin.

53. Improving physics-informed neural networks with meta-learned optimization. arXiv, 2023. paper

    Alex Bihlo.

54. MetaPhysiCa: OOD robustness in physics-informed machine learning. arXiv, 2023. paper

    S Chandra Mouli, Muhammad Ashraful Alam, and Bruno Ribeiro.

55. HomPINNs: Homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. arXiv, 2023. paper

    Haoyang Zheng, Yao Huang, Ziyang Huang, Wenrui Hao, and Guang Lin.

56. iPINNs: Incremental learning for physics-informed neural networks. arXiv, 2023. paper

    Aleksandr Dekhovich, Marcel H.F. Sluiter, David M.J. Tax, and Miguel A. Bessa.

57. Global convergence of deep Galerkin and PINNs methods for solving partial differential equations. arXiv, 2023. paper

    Francisco Eiras, Adel Bibi, Rudy Bunel, Krishnamurthy Dj Dvijotham, Philip Torr, and M. Pawan Kumar.

58. Provably correct physics-informed neural networks. arXiv, 2023. paper

    Deqing Jiang, Justin Sirignano, and Samuel N. Cohen.

59. Predictive limitations of physics-informed neural networks in vortex shedding. arXiv, 2023. paper

    Pi-Yueh Chuang and Lorena A. Barba.

60. Residual-based error bound for physics-informed neural networks. arXiv, 2023. paper

    Shuheng Liu, Xiyue Huang, and Pavlos Protopapas.

61. Automatic boundary fitting framework of boundary dependent physics-informed neural network solving partial differential equation with complex boundary conditions. Computer Methods in Applied Mechanics and Engineering, 2023. paper

    Yuchen Xie, Yu Ma, and Yahui Wang.

62. Solving a class of multi-scale elliptic PDEs by means of Fourier-based mixed physics informed neural networks. arXiv, 2023. paper

    Xi'an Li, Jinran Wu, Zhi-Qin John Xu, and You-Gan Wang.

63. Separable physics informed neural networks. arXiv, 2023. paper

    Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park.

64. Achieving high accuracy with PINNs via energy natural gradient descent. ICML, 2023. paper

    Johannes Müller and Marius Zeinhofer.

65. Gradient descent finds the global optima of two-layer physics-informed neural networks. ICML, 2023. paper

    Yihang Gao, Yiqi Gu, and Michael Ng.

66. Residual-based attention and connection to information bottleneck theory in PINNs. arXiv, 2023. paper

    Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, and George Em Karniadakis.

67. Auxiliary-tasks learning for physics-informed neural network-based partial differential equations solving. arXiv, 2023. paper

    Junjun Yan, Xinhai Chen, Zhichao Wang, Enqiang Zhou, and Jie Liu.

68. Tackling the curse of dimensionality with physics-informed neural networks. arXiv, 2023. paper

    Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, and Kenji Kawaguchi.

1. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. NMI, 2021. paper

   Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis.

2. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. SA, 2021. paper

   Wang Sifan, Hanwen Wang, and Paris Perdikaris.

3. Deep transfer operator learning for partial differential equations under conditional shift. NMI, 2022. paper

   Somdatta Goswami, Katiana Kontolati, Michael D. Shields, and George Em Karniadakis.

4. Variable-input deep operator networks. arXiv, 2022. paper

   Michael Prasthofer, Tim De Ryck, and Siddhartha Mishra.

5. MIONet: Learning multiple-input operators via tensor product. arXiv, 2022. paper

   Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.

6. Error estimates for DeepONets: A deep learning framework in infinite dimensions. Transactions of Mathematics and Its Applications, 2022. paper

   Samuel Lanthaler, Siddhartha Mishra, and George E Karniadakis.

7. Long-time integration of parametric evolution equations with physics-informed DeepONets. arXiv, 2021. paper

   Sifan Wang and Paris Perdikaris.

8. Improved architectures and training algorithms for deep operator networks. Journal of Scientific Computing, 2022. paper

   Sifan Wang, Hanwen Wang, and Paris Perdikaris.

9. SVD perspectives for augmenting DeepONet flexibility and interpretability. arXiv, 2022. paper

   Simone Venturi and Tiernan Casey.

10. Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs. arXiv, 2021. paper

    Guang Lin, Christian Moya, and Zecheng Zhang.

11. Bi-fidelity modeling of uncertain and partially unknown systems using DeepONet. arXiv, 2022. paper

    Subhayan De, Matthew Reynolds, Malik Hassanaly, Ryan N. King, and Alireza Doostan.

12. MultiAuto-DeepONet: A multi-resolution autoencoder DeepONet for nonlinear dimension reduction, uncertainty quantification and operator learning of forward and inverse stochastic problems. arXiv, 2022. paper

    Jiahao Zhang, Shiqi Zhang, and Guang Lin.

13. Transfer learning enhanced DeepONet for long-time prediction of evolution equations. arXiv, 2022. paper

    Wuzhe Xu, Yulong Lu, and Li Wang.

14. B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD. JCP, 2023. paper

    Guang Lin, Christian Moy, and Zecheng Zhang.

15. VB-DeepONet: A Bayesian operator learning framework for uncertainty quantification. Engineering Applications of Artificial Intelligence, 2023. paper

    Shailesh Garg and Souvik Chakraborty.

16. Sequential deep learning operator network (S-DeepONet) for time-dependent loads. arXiv, 2023. paper

    Jaewan Park, Shashank Kushwaha, Junyan He, Seid Koric, Diab Abueidda, and Iwona Jasiuk.

17. Asymptotic-preserving convolutional DeepONets capture the diffusive behavior of the multiscale linear transport equations. arXiv, 2023. paper

    Keke Wu, Xiong-bin Yan, Shi Jin, and Zheng Ma.

1. Fourier neural operator for parametric partial differential equations. ICLR, 2021. paper

   Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

2. On universal approximation and error bounds for Fourier neural operators. JMLR, 2021. paper

   Nikola Kovachki, Samuel Lanthaler, and Siddhartha Mishra.

3. HyperFNO: Improving the generalization behavior of Fourier neural operators. NIPS, 2022. paper

   Francesco Alesiani, Makoto Takamoto, and Mathias Niepert.

4. Neural operator: Graph kernel network for partial Differential equations. arXiv, 2020. paper

   Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

5. Fourier neural operator with learned deformations for PDEs on general geometries. arXiv, 2022. paper

   Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, and Anima Anandkumar.

6. Multipole graph neural operator for parametric partial differential equations. NIPS, 2020. paper

   Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

7. Fast sampling of diffusion models via operator learning. NIPS, 2022. paper

   Hongkai Zheng, Weili Nie, Arash Vahdat, Kamyar Azizzadenesheli, and Anima Anandkumar.

8. Factorized Fourier neural operators. ICLR, 2023. paper

   Alasdair Tran, Alexander Mathews, Lexing Xie, and Cheng Soon Ong.

9. Model inversion for spatio-temporal processes using the Fourier neural operator. NIPS, 2023. paper

   Dan MacKinlay, Dan Pagendam, Petra M. Kuhnert, Tao Cui, David Robertson, and Sreekanth Janardhanan.

10. Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Huaiqian You, Quinn Zhang, Colton J. Ross, Chung-Hao Lee, and Yue Yu.

11. On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2021. paper

    Sifan Wang, Hanwen Wang, and Paris Perdikaris.

12. Semi-supervised learning of partial differential operators and dynamical flows. arXiv, 2022. paper

    Michael Rotman, Amit Dekel, Ran Ilan Ber, Lior Wolf, and Yaron Oz.

13. Non-equispaced Fourier neural solvers for PDEs. arXiv, 2022. paper

    Haitao Lin, Lirong Wu, Yongjie Xu, Yufei Huang, Siyuan Li, Guojiang Zhao, Stan Z, and Li Cari.

14. Incremental spectral learning Fourier neural operator. arXiv, 2022. paper

    Jiawei Zhao, Robert Joseph George, Yifei Zhang, Zongyi Li, and Anima Anandkumar.

15. Fourier continuation for exact derivative computation in physics-informed neural operators. arXiv, 2022. paper

    Haydn Maust, Zongyi Li, Yixuan Wang, Daniel Leibovici, Oscar Bruno, Thomas Hou, and Anima Anandkumar.

16. Non-equispaced Fourier neural solvers for PDEs. arXiv, 2023. paper

    Haitao Lin, Lirong Wu, Yongjie Xu, Yufei Huang, Siyuan Li, Guojiang Zhao, Stan Z, and Li Cari.

17. Learning-based solutions to nonlinear hyperbolic PDEs: Empirical insights on generalization errors. arXiv, 2023. paper

    Bilal Thonnam Thodi, Sai Venkata Ramana Ambadipudi, and Saif Eddin Jabari.

18. Domain agnostic Fourier neural operators. arXiv, 2023. paper

    Ning Liu, Siavash Jafarzadeh, and Yue Yu.

19. Spherical Fourier neural operators: Learning stable dynamics on the sphere. ICML, 2023. paper

    Boris Bonev, Thorsten Kurth, Christian Hundt, Jaideep Pathak, Maximilian Baust, Karthik Kashinath, and Anima Anandkumar.

20. Group equivariant Fourier neural operators for partial differential equations. ICML, 2023. paper

    Jacob Helwig, Xuan Zhang, Cong Fu, Jerry Kurtin, Stephan Wojtowytsch, and Shuiwang Ji.

21. Speeding up Fourier neural operators via mixed precision. arXiv, 2023. paper

    Colin White, Renbo Tu, Jean Kossaifi, Gennady Pekhimenko, Kamyar Azizzadenesheli, and Anima Anandkumar.

1. Message passing neural PDE solvers. ICLR, 2022. paper

   Johannes Brandstetter, Daniel E. Worrall, and Max Welling.

2. Predicting physics in mesh-reduced space with temporal attention. ICLR, 2022. paper

   Xu Han, Han Gao, Tobias Pfaff, Jianxun Wang, and Liping Liu.

3. Learning mesh-based simulation with graph networks. ICLR, 2021. paper

   Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter Battaglia.

4. Learning large-scale subsurface simulations with a hybrid graph network simulator. KDD, 2022. paper

   Tailin Wu, Qinchen Wang, Yinan Zhang, Rex Ying, Kaidi Cao, Rok Sosič, Ridwan Jalali, Hassan Hamam, Marko Maucec, and Jure Leskovec.

5. Unravelling the performance of physics-informed graph neural networks for dynamical systems. NIPS, 2022. paper

   Abishek Thangamuthu, Gunjan Kumar, Suresh Bishnoi, Ravinder Bhattoo, N M Anoop Krishnan, and Sayan Ranu.

6. Learning the solution operator of boundary value problems using graph neural networks. ICML, 2022. paper

   Winfried Lötzsch, Simon Ohler, and Johannes S. Otterbach.

7. Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   Han Gao, Matthew J.Zahr, and Jianxun Wang.

8. Modular flows: Differential molecular generation. NIPS, 2022. paper

   Yogesh Verma, Samuel Kaski, Markus Heinonen, and Vikas Garg.

9. Learning to solve PDE-constrained inverse problems with graph networks. ICML, 2022. paper

   Zhao Qingqing, David B. Lindell, and Gordon Wetzstein.

10. Physics-embedded neural networks: E(n)-equivariant graph neural PDE solvers. NIPS, 2022. paper

    Masanobu Horie and Naoto Mitsume.

11. PDE-GCN: Novel architectures for graph neural networks motivated by partial differential equations. ICLR, 2021. paper

    Moshe Eliasof, Eldad Haber, and Eran Treister.

12. Physics-aware difference graph networks for sparsely-observed dynamics. ICLR, 2020. paper

    Sungyong Seo, Chuizheng Meng, and Yan Liu.

13. Combining differentiable PDE solvers and graph neural networks for fluid flow prediction. ICML, 2022. paper

    Filipe de Avila Belbute-Peres, Thomas D. Economon, and J. Zico Kolter.

14. Learning continuous-time PDEs from sparse data with graph neural networks. ICLR, 2021. paper

    Valerii Iakovlev, Markus Heinonen, and Harri Lähdesmäki.

15. Learning to simulate complex physics with graph networks. ICML, 2020. paper

    Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter W. Battaglia.

16. Multi-scale physical representations for approximating PDE solutions with graph neural operators. ICLR, 2022. paper

    Léon Migus, Yuan Yin, Jocelyn Ahmed Mazari, and Patrick Gallinari.

17. DS-GPS: A deep statistical graph Poisson solver (for faster CFD simulations). NIPS, 2022. paper

    Matthieu Nastorg, Marc Schoenauer, Guillaume Charpiat, Thibault Faney, Jean-Marc Gratien, and Michele-Alessandro Bucci.

18. GRAND: Graph neural diffusion. ICML, 2021. paper

    Benjamin Paul Chamberlain, James Rowbottom, Maria I. Gorinova, Stefan D Webb, Emanuele Rossi, and Michael M. Bronstein.

19. GRAND++: Graph neural diffusion with a source term. ICML, 2022. paper

    Matthew Thorpe, Tan Minh Nguyen, Hedi Xia, Thomas Strohmer, Andrea Bertozzi, Stanley Osher, and Bao Wang.

20. Neural networks trained to solve differential equations learn general representations. NIPS, 2018. paper

    Martin Magill, Faisal Qureshi, and Hendrick de Haan.

21. Graph element networks: Adaptive, structured computation and memory. ICML, 2019. paper

    Ferran Alet, Adarsh Keshav Jeewajee, Maria Bauza Villalonga, Alberto Rodriguez, Tomas Lozano-Perez, and Leslie Kaelbling.

22. Physics-constrained unsupervised learning of partial differential equations using meshes. arXiv, 2022. paper

    Mike Y. Michelis and Robert K. Katzschmann.

23. Neural PDE solvers for irregular domains. arXiv, 2022. paper

    Biswajit Khara, Ethan Herron, Zhanhong Jiang, Aditya Balu, Chih-Hsuan Yang, Kumar Saurabh, Anushrut Jignasu, Soumik Sarkar, Chinmay Hegde, Adarsh Krishnamurthy, and Baskar Ganapathysubramanian.

24. Bi-stride multi-scale graph neural network for mesh-based physical simulation. arXiv, 2022. paper

    Yadi Cao, Menglei Chai, Minchen Li, and Chenfanfu Jiang.

25. Learning time-dependent PDE solver using message passing graph neural networks. arXiv, 2022. paper

    Pourya Pilva and Ahmad Zareei.

26. On the robustness of graph neural diffusion to topology perturbations. arXiv, 2022. paper

    Yang Song, Qiyu Kang, Sijie Wang, Zhao Kai, and Wee Peng Tay.

27. STONet: A neural-operator-driven spatio-temporal network. arXiv, 2022. paper

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28. PhyGNNet: Solving spatiotemporal PDEs with physics-informed graph neural network. arXiv, 2022. paper

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29. Differentiable physics-informed graph networks. arXiv, 2019. paper

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30. MG-GNN: Multigrid graph neural networks for learning multilevel domain decomposition methods. ICML, 2023. paper

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31. Multi-scale message passing neural PDE solvers. arXiv, 2023. paper

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32. An implicit GNN solver for Poisson-like problems. arXiv, 2023. paper

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33. GNN-based physics solver for time-independent PDEs. arXiv, 2023. paper

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35. Long-short-range message-passing: A physics-informed framework to capture non-local interaction for scalable molecular dynamics simulation. arXiv, 2023. paper

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36. A graph convolutional autoencoder approach to model order reduction for parametrized PDEs. arXiv, 2023. paper

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37. GAD-NR: Graph anomaly detection via neighborhood reconstruction. arXiv, 2023. paper

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38. GPINN: Physics-informed neural network with graph embedding. arXiv, 2023. paper

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1. Learning Green's functions associated with time-dependent partial differential equations. JMLR, 2022. paper

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2. BI-GreenNet: Learning Green's functions by boundary integral network. arXiv, 2022. paper

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3. DeepGreen: Deep learning of Green’s functions for nonlinear boundary value problems. Scientific Reports, 2021. paper

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4. Data-driven discovery of Green’s functions with human-understandable deep learning. Scientific Reports, 2022. paper

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5. Data-driven discovery of Green's functions. Doctoral Dissertation, 2022. Ph.D.

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6. Principled interpolation of Green's functions learned from data. arXiv, 2022. paper

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7. Deep generalized Green's functions. arXiv, 2023. paper

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8. Operator approximation of the wave equation based on deep learning of Green’s function. arXiv, 2023. paper

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1. Composing partial differential equations with physics-aware neural networks. ICML, 2022. paper

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2. Learning the dynamics of physical systems from sparse observations with finite element networks. ICLR, 2022. paper

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3. A unified hard-constraint framework for solving geometrically complex PDEs. NIPS, 2022. paper

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4. LSH-SMILE: Locality sensitive Hashing accelerated simulation and learning. NIPS, 2021. paper

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5. Amortized finite element analysis for fast PDE-constrained optimization. ICML, 2020. paper

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6. Learning neural PDE solvers with convergence guarantees. ICLR, 2019. paper

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7. Hybrid finite difference with the physics-informed neural network for solving PDE in complex geometries. arXiv, 2022. paper

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8. Multilayer perceptron-based surrogate models for finite element analysis. arXiv, 2022. paper

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1. PDE-Net: Learning PDEs from data. ICML, 2018. paper

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2. PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network. JCP, 2019. paper

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3. Physics-informed CNNs for super-resolution of sparse observations on dynamical systems. NIPS, 2022. paper

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4. Deep-pretrained-FWI: Combining supervised learning with physics-informed neural network. NIPS, 2022. paper

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5. Learning time-dependent PDEs with a linear and nonlinear separate convolutional neural network. JCP, 2022. paper

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6. PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs. JCP, 2022. paper

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7. Spline-PINN: Approaching PDEs without data using fast, physics-informed Hermite-Spline CNNs. AAAI, 2019. paper

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8. Deep convolutional Ritz method: Parametric PDE surrogates without labeled data. arXiv, 2022. paper

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9. Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems. arXiv, 2022. paper

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10. Phase2Vec: Dynamical systems embedding with a physics-informed convolutional network. arXiv, 2022. paper

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11. Numerical approximation based on deep convolutional neural network for high-dimensional fully nonlinear merged PDEs and 2BSDEs. arXiv, 2022. paper

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12. SplineCNN: Fast geometric deep learning with continuous B-spline kernels. CVPR, 2018. paper

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13. Physics-informed deep super-resolution for spatiotemporal data. arXiv, 2022. paper

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14. MeshFreeFLowNet: A physics-constrained deep continuous space-time super-resolution framework. SC20, 2020. paper

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15. Convolutional neural operators. arXiv, 2023. paper

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16. An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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17. Clifford neural layers for PDE modeling. ICLR, 2023. paper

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18. Neural partial differential equations with functional convolution. arXiv, 2023. paper

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19. Multilevel CNNs for parametric PDEs. arXiv, 2023. paper

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20. Encoding physics to learn reaction–diffusion processes. NMI, 2023. paper

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1. Integral autoencoder network for discretization-invariant learning. JMLR, 2022. paper

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2. Variational autoencoding neural operators. arXiv, 2023. paper

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3. PI-VEGAN: Physics informed variational embedding generative adversarial networks for stochastic differential equations. arXiv, 2023. paper

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1. Multiwavelet-based operator learning for differential equations. NIPS, 2021. paper

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2. On the representation of solutions to elliptic PDEs in Barron space. NIPS, 2021. paper

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3. Low-rank registration based manifolds for convection-dominated PDEs. AAAI, 2021. paper

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4. Isogeometric neural networks: A new deep learning approach for solving parameterized partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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5. A nonlocal physics-informed deep learning framework using the peridynamic differential operator. Computer Methods in Applied Mechanics and Engineering, 2021. paper

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6. Kernel flows: From learning kernels from data into the abyss. JCP, 2019. paper

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7. On neurosymbolic solutions for PDEs. arXiv, 2022. paper

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8. An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis. arXiv, 2022. paper

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9. Nonparametric learning of kernels in nonlocal operators. arXiv, 2022. paper

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10. Spectral neural operators. arXiv, 2022. paper

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11. NOMAD: Nonlinear manifold decoders for operator learning. arXiv, 2022. paper

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12. U-NO: U-shaped neural operators. arXiv, 2022. paper

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13. Wavelet neural operator: A neural operator for parametric partial differential equations. arXiv, 2022. paper

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14. Pseudo-differential integral operator for learning solution operators of partial differential equations. arXiv, 2022. paper

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15. Nonlinear reconstruction for operator learning of PDEs with discontinuities. arXiv, 2022. paper

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16. GeONet: A neural operator for learning the Wasserstein geodesic. arXiv, 2022. paper

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17. Render unto numerics: Orthogonal polynomial neural operator for PDEs with non-periodic boundary conditions. arXiv, 2022. paper

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18. DOSNet as a non-black-box PDE solver: When deep learning meets operator splitting. arXiv, 2022. paper

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19. Guiding continuous operator learning through physics-based boundary constraints. arXiv, 2022. paper

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20. BelNet: Basis enhanced learning, a mesh-free neural operator. arXiv, 2022. paper

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21. INO: Invariant neural operators for learning complex physical systems with momentum conservation. arXiv, 2022. paper

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22. BINN: A deep learning approach for computational mechanics problems based on boundary integral equations. arXiv, 2023. paper

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23. Koopman neural operator as a mesh-free solver of non-linear partial differential equations. arXiv, 2023. paper

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24. Physics-informed Koopman network. arXiv, 2022. paper

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25. Deep operator learning lessens the curse of dimensionality for PDEs. arXiv, 2023. paper

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26. Algorithmically designed artificial neural networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. arXiv, 2023. paper

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27. Entropy-dissipation informed neural network for McKean-Vlasov type. arXiv, 2023. paper

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28. A neural PDE solver with temporal stencil modeling. ICML, 2023. paper

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29. Neural operator learning for long-time integration in dynamical systems with recurrent neural networks. arXiv, 2023. paper

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30. Coupled multiwavelet operator learning for coupled differential equations. ICLR, 2023. paper

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31. LNO: Laplace neural operator for solving differential equations. arXiv, 2023. paper

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32. Vandermonde neural operator. arXiv, 2023. paper

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33. Energy-dissipative evolutionary deep operator neural networks. arXiv, 2023. paper

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34. Physics informed WNO. arXiv, 2023. paper

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35. Corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems. arXiv, 2023. paper

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36. HNO: Hyena neural operator for solving PDEs. arXiv, 2023. paper

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37. Finite element operator network for solving parametric PDEs. arXiv, 2023. paper

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38. PDE-Refiner: Achieving accurate long rollouts with neural PDE solvers. arXiv, 2023. paper

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1. Data-driven discovery of partial differential equations. SA, 2017. paper

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2. Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression. NC, 2021. paper

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3. Discovering nonlinear PDEs from scarce data with physics-encoded learning. ICLR, 2022. paper

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4. Differential spectral normalization (DSN) for PDE discovery. AAAI, 2021. paper

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5. Learning differential operators for interpretable time series modeling. KDD, 2022. paper

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6. Learning emergent partial differential equations in a learned emergent space. NC, 2022. paper

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7. Physics-informed learning of governing equations from scarce data. NC, 2021. paper

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8. Machine learning hidden symmetries. PRL, 2022. paper

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9. Efficient learning of sparse and decomposable PDEs using random projection. UAI, 2022. paper

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10. Data-driven discovery of partial differential equation models with latent variables. Physical Review E, 2019. paper

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11. Physics constrained learning for data-driven inverse modeling from sparse observations. Physical Review E, 2019. paper

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12. Deep neural network modeling of unknown partial differential equations in nodal space. JCP, 2022. paper

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13. DeepMOD: Deep learning for model discovery in noisy data. JCP, 2021. paper

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14. Theory-guided hard constraint projection (HCP): A knowledge-based data-driven scientific machine learning method. JCP, 2021. paper

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17. Data-driven deep learning of partial differential equations in modal space. JCP, 2020. paper

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18. DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm. JCP, 2020. paper

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19. Learning nonlocal constitutive models with neural networks. Computer Methods in Applied Mechanics and Engineering, 2021. paper

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20. Data-driven identification of parametric partial differential equations. SIAM Journal on Applied Dynamical Systems, 2019. paper

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21. PDE-READ: Human-readable partial differential equation discovery using deep learning. Neural Networks, 2022. paper

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22. Discover: Deep identification of symbolic open-form PDEs via enhanced reinforcement-learning. arXiv, 2022. paper

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23. ModLaNets: Learning generalisable dynamics via modularity and physical inductive bias. ICML, 2022. paper

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24. Robust discovery of partial differential equations in complex situations. Physical Review Research, 2021. paper

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25. Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks. JCP, 2020. paper

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26. Deep learning and inverse discovery of polymer self-consistent field theory inspired by physics-informed neural networks. Physical Review E, 2022. paper

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27. Data-driven solutions and parameter discovery of the Sasa–Satsuma equation via the physics-informed neural networks method. Physica D, 2022. paper

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28. Reliable extrapolation of deep neural operators informed by physics or sparse observations. arXiv, 2022. paper

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29. Neural operator with regularity structure for modeling dynamics driven by SPDEs. arXiv, 2022. paper

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30. A PINN approach to symbolic differential operator discovery with sparse data. arXiv, 2022. paper

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31. WeakIdent: Weak formulation for identifying differential equations using narrow-fit and trimming. arXiv, 2022. paper

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32. Predicting parametric spatiotemporal dynamics by multi-resolution PDE structure-preserved deep learning. arXiv, 2022. paper

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33. Data-driven modeling of Landau damping by physics-informed neural networks. arXiv, 2022. paper

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34. Discovering governing equations in discrete systems using PINNs. arXiv, 2022. paper

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35. Physics-guided generative adversarial network to learn physical models. arXiv, 2023. paper

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36. PDE-Learn: Using deep learning to discover partial differential equations from noisy, limited data. arXiv, 2022. paper

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37. PiSL: Physics-informed Spline Learning for data-driven identification of nonlinear dynamical systems. MSSP, 2023. paper

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38. Learning physical models that can respect conservation laws. arXiv, 2023. paper

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39. Data-driven discovery of intrinsic dynamics. NMI, 2022. paper

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40. Symbolic regression for PDEs using pruned differentiable programs. ICLR, 2023. paper

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41. Symbolic physics learner: Discovering governing equations via Monte Carlo tree search. ICLR, 2023. paper

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42. Learning neural constitutive laws from motion observations for generalizable PDE dynamics. ICML, 2023. paper

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43. Learning partial differential equations in reproducing kernel Hilbert spaces. JMLR, 2023. paper

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44. Finite expression methods for discovering physical laws from data. arXiv, 2023. paper

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45. Physics-informed representation learning for emergent organization in complex dynamical systems. arXiv, 2023. paper

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46. An analysis of universal differential equations for data-driven discovery of ordinary differential equations. arXiv, 2023. paper

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47. TaylorPDENet: Learning PDEs from non-grid data. arXiv, 2023. paper

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48. Learning of discrete models of variational PDEs from data. arXiv, 2023. paper

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49. Towards true discovery of the differential equations. arXiv, 2023. paper

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1. Machine learning–accelerated computational fluid dynamics. PNAS, 2021. paper

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2. Learning data-driven discretization for partial differential equations. PNAS, 2019. paper

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3. Solving high-dimensional partial differential equations using deep learning. PNAS, 2018. paper

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4. Enhancing computational fluid dynamics with machine learning. NCS, 2022. paper

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5. Solving high-dimensional parabolic PDEs using the tensor train format. ICML, 2021. paper

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6. A hybrid reduced basis and machine-learning algorithm for building surrogate models: A first application to electromagnetism. NIPS, 2022. paper

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7. Numerically solving parametric families of high-dimensional Kolmogorov partial differential equations via deep learning. NIPS, 2020. paper

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8. Nonlocal kernel network (NKN): A stable and resolution-independent deep neural network. JCP, 2022. paper

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9. On computing the hyperparameter of extreme learning machines: Algorithm and application to computational PDEs, and comparison with classical and high-order finite elements. JCP, 2022. paper

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10. Int-Deep: A deep learning initialized iterative method for nonlinear problems. JCP, 2022. paper

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11. DeLISA: Deep learning based iteration scheme approximation for solving PDEs. JCP, 2022. paper

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12. Physics-informed machine learning for reduced-order modeling of nonlinear problems. JCP, 2021. paper

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13. SelectNet: Self-paced learning for high-dimensional partial differential equations. JCP, 2021. paper

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14. Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs. JCP, 2020. paper

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17. Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets. Computer Methods in Applied Mechanics and Engineering, 2021. paper

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19. Reduced order modeling for parameterized time-dependent PDEs using spatially and memory aware deep learning. JCP, 2021. paper

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20. GCN-FFNN: A two-stream deep model for learning solution to partial differential equations. Neurocomputing, 2022. paper

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21. Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs. Journal of Scientific Computing, 2021. paper

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23. A model-constrained tangent slope learning approach for dynamical systems. arXiv, 2022. paper

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32. Multiscale attention via wavelet neural operators for vision Transformers. arXiv, 2023. paper

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34. SHoP: A deep learning framework for solving high-order partial differential equations. arXiv, 2023. paper

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35. A Neural RDE-based model for solving path-dependent PDEs. arXiv, 2023. paper

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36. Global universal approximation of functional input maps on weighted spaces. arXiv, 2023. paper

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37. Accelerating explicit time-stepping with spatially variable time steps through machine learning. Journal of Scientific Computing, 2023. paper

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40. Fully probabilistic deep models for forward and inverse problems in parametric PDEs. JCP, 2023. paper

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42. Element learning: A systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer. arXiv, 2023. paper

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1. Neural rough differential equations for long time series. ICML, 2021. paper

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2. LEADS: Learning dynamical systems that generalize across environments. NIPS, 2021. paper

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11. Stochastic physics-informed neural ordinary differential equations. arXiv, 2021. paper

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12. A stable and scalable method for solving initial value PDEs with neural networks. ICLR, 2023. paper

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18. Neural signature kernels as infinite-width-depth-limits of controlled ResNets. ICML, 2023. paper

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19. AbODE: Ab initio antibody design using conjoined ODEs. ICML, 2023. paper

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21. Predicting ordinary differential equations with Transformers. ICML, 2023. paper

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1. Prompting in-context operator learning with sensor data, equations, and natural language. arXiv, 2023. paper

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1. PDEBench: An extensive benchmark for scientific machine learning. NIPS, 2022. paper

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4. An extensible benchmarking graph-mesh dataset for studying steady-state incompressible Navier-Stokes equations. ICLR, 2022. paper

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10. PINNacle: A comprehensive benchmark of physics-informed neural networks for solving PDEs. arXiv, 2023. paper

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1. Characterizing possible failure modes in physics-informed neural networks. NIPS, 2021. paper

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2. Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing, 2021. paper

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3. When and why PINNs fail to train: A neural tangent kernel perspective. JCP, 2022. paper

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4. When do extended physics-informed neural networks (XPINNs) improve generalization? SIAM Journal on Scientific Computing, 2022. paper

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5. MARS: A method for the adaptive removal of stiffness in PDEs. JCP, 2022. paper

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6. Learning similarity metrics for numerical simulations. ICML, 2020. paper

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7. A curriculum-training-based strategy for distributing collocation points during physics-informed neural network training. NIPS, 2021. paper

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8. Parametric complexity bounds for approximating PDEs with neural networks. NIPS, 2021. paper

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9. Respecting causality is all you need for training physics-informed neural networks. arXiv, 2021. paper

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10. CP-PINNS: Changepoints detection in PDEs using physics informed neural networks with total-variation penalty. arXiv, 2022. paper

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11. Stochastic projection based approach for gradient free physics informed learning. arXiv, 2022. paper

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12. Understanding the difficulty of training physics-informed neural networks on dynamical systems. arXiv, 2022. paper

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13. Mitigating learning complexity in physics and equality constrained artificial neural networks. arXiv, 2022. paper

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14. Improved training of physics-informed neural networks with model ensembles. arXiv, 2022. paper

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15. The cost-accuracy trade-off in operator learning with neural networks. arXiv, 2022. paper

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16. Neural tangent kernel analysis of PINN for advection-diffusion equation. arXiv, 2022. paper

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17. Separable PINN: Mitigating the curse of dimensionality in physics-informed neural networks. NIPS, 2022. paper

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18. A curriculum-training-based strategy for distributing collocation points during physics-informed neural network training. NIPS, 2022. paper

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19. Robustness of physics-informed neural networks to noise in sensor data. arXiv, 2022. paper

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20. Investigations on convergence behaviour of physics informed neural networks across spectral ranges and derivative orders. arXiv, 2023. paper

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21. Stochastic projection based approach for gradient free physics informed learning. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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22. Temporal consistency loss for physics-informed neural networks. arXiv, 2023. paper

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23. Can physics-informed neural networks beat the finite element method? arXiv, 2023. paper

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24. LSA-PINN: Linear boundary connectivity loss for solving PDEs on complex geometry. arXiv, 2023. paper

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25. On the Hyperparameters influencing a PINN’s generalization beyond the training domain. arXiv, 2023. paper

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26. DPM: A novel training method for physics-informed neural networks in extrapolation. AAAI, 2021. paper

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27. Guiding continuous operator learning through physics-based boundary constraints. ICLR, 2023. paper

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28. A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions. arXiv, 2023. paper

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29. Machine learning for elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality. ICLR, 2022. paper

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30. Probing optimisation in physics-informed neural networks. ICLR, 2023. paper

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31. Nearly optimal VC-dimension and Pseudo-dimension bounds for deep neural network derivatives. arXiv, 2023. paper

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32. PDE+: Enhancing generalization via PDE with adaptive distributional diffusion. arXiv, 2023. paper

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33. Towards foundation models for scientific machine learning: Characterizing scaling and transfer behavior. arXiv, 2023. paper

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34. Stability of implicit neural networks for long-term forecasting in dynamical systems. ICLR, 2023. paper

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35. Understanding and mitigating extrapolation failures in physics-informed neural networks. arXiv, 2023. paper

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36. Physics-informed neural network based on a new adaptive gradient descent algorithm for solving partial differential equations of flow problems. Physics of Fluids, 2023. paper

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37. CrunchGPT: A chatGPT assisted framework for scientific machine learning. arXiv, 2023. paper

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38. The curse of dimensionality in operator learning. arXiv, 2023. paper

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39. Inverse evolution layers: Physics-informed regularizers for deep neural networks. arXiv, 2023. paper

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40. A discretization-invariant extension and analysis of some deep operator networks. arXiv, 2023. paper

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41. Modeling accurate long rollouts with temporal neural PDE solvers. ICML, 2023. paper

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42. Positional embeddings for solving PDEs with evolutional deep neural networks. arXiv, 2023. paper

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43. Learning specialized activation functions for physics-informed neural networks. arXiv, 2023. paper

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44. Size lowerbounds for deep operator networks. arXiv, 2023. paper

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1. Learning operators with coupled attention. JMLR, 2022. paper

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2. Choose a Transformer: Fourier or Galerkin. NIPS, 2021. paper

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3. Predicting physics in mesh-reduced space with temporal attention. ICLR, 2022. paper

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4. SiT: Simulation transformer for particle-based physics simulation. ICLR, 2022. paper

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5. Physics-informed long-sequence forecasting from multi-resolution spatiotemporal data. IJCAI, 2022. paper

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6. TransFlowNet: A physics-constrained Transformer framework for spatio-temporal super-resolution of flow simulations. Journal of Computational Science, 2022. paper

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7. Self-adaptive physics-informed neural networks using a soft attention mechanism. AAAI-MLPS, 2021. paper

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8. Transformer for partial differential equations' operator learning. arXiv, 2022. paper

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9. Physics-informed attention-based neural network for hyperbolic partial differential equations: Application to the Buckley–Leverett problem. Scientific Reports, 2022. paper

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10. Self-adaptive physics-informed neural networks using a soft attention mechanism. AAAI-MLPS, 2021. paper

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11. Nonlinear reconstruction for operator learning of PDEs with discontinuities. ICLR, 2023. paper

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12. GNOT: A general neural operator transformer for operator learning. ICML, 2023. paper

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13. In-context operator learning for differential equation problems. arXiv, 2023. paper

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14. Learning neural PDE solvers with parameter-guided channel attention. ICML, 2023. paper

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15. Physics informed token Transformer. arXiv, 2023. paper

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1. Neural implicit flow: A mesh-agnostic dimensionality reduction paradigm of spatio-temporal data. arXiv, 2022. paper

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2. CROM: Continuous reduced-order modeling of PDEs using implicit neural representations. ICLR, 2023. paper

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3. MAgNet: Mesh agnostic neural PDE solver. NIPS, 2022. paper

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4. NTopo: Mesh-free topology optimization using implicit neural representations. NIPS, 2021. paper

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5. ContactNets: Learning discontinuous contact dynamics with smooth, implicit representations. ICLR, 2020. paper

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6. Continuous PDE dynamics forecasting with implicit neural representations. ICLR, 2023. paper

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7. Operator learning with neural fields: Tackling PDEs on general geometries. arXiv, 2023. paper

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8. Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature. arXiv, 2023. paper

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9. Implicit neural spatial representations for time-dependent PDEs. ICML, 2023. paper

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1. PDE-driven spatiotemporal disentanglement. ICLR, 2021. paper

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2. Disentangling physical dynamics from unknown factors for unsupervised video prediction. CVPR, 2020. paper

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1. Meta-auto-decoder for solving parametric partial differential equations. NIPS, 2022. paper

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2. Transfer learning with physics-informed neural networks for efficient simulation of branched flows. NIPS, 2022. paper

   Raphaël Pellegrin, Blake Bullwinkel, Marios Mattheakis, and Pavlos Protopapas.

3. Identifying physical law of hamiltonian systems via meta-learning. ICLR, 2021. paper

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4. One-shot learning for solution operators of partial differential equations. ICLR, 2021. paper

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5. A metalearning approach for physics-informed neural networks (PINNs): Application to parameterized PDEs. JCP, 2023. paper

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6. Meta-MgNet: Meta multigrid networks for solving parameterized partial differential equations. JCP, 2022. paper

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7. Mosaic flows: A transferable deep learning framework for solving PDEs on unseen domains. Computer Methods in Applied Mechanics and Engineering, 2022. paper

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8. Meta-learning PINN loss functions. JCP, 2022. paper

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9. HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks. NIPS, 2021. paper

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10. Adversarial multi-task learning enhanced physics-informed neural networks for solving partial differential equations. IJCNN, 2022. paper

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11. Transfer physics informed neural network: A new framework for distributed physics informed neural networks via parameter sharing. Engineering with Computers, 2022. paper

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12. Meta-PDE: Learning to solve PDEs quickly without a mesh. arXiv, 2022. paper

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13. SVD-PINNs: Transfer learning of physics-informed neural networks via singular value decomposition. arXiv, 2022. paper

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14. Physics-informed neural networks (PINNs) for parameterized PDEs: A meta-learning approach. arXiv, 2021. paper

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15. Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs. arXiv, 2022. paper

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16. Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios. arXiv, 2022. paper

    Chen Xu, Ba Trung Cao, Yong Yuan, and Günther Meschke.

17. TransNet: Transferable neural networks for partial differential equations. arXiv, 2023. paper

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18. Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems. arXiv, 2023. paper

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19. GPT-PINN: Generative pre-trained physics-informed neural networks toward non-intrusive meta-learning of parametric PDEs. arXiv, 2023. paper

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20. A metalearning approach for physics-informed neural networks (PINNs): Application to parameterized PDEs. JCP, 2023. paper

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21. Gradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equations. arXiv, 2023. paper

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22. Towards foundation models for scientific machine learning: Characterizing scaling and transfer behavior. arXiv, 2023. paper

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23. Adaptive transfer learning for PINN. JCP, 2023. paper

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24. Meta learning of interface conditions for multi-domain physics-informed neural networks. ICML, 2023. paper

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25. A sequential meta-transfer (SMT) learning to combat complexities of physics-informed neural networks: Application to composites autoclave processing. arXiv, 2023. paper

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1. Auto-PINN: Understanding and optimizing physics-informed neural architecture. arXiv, 2022. paper

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2. Building high accuracy emulators for scientific simulations with deep neural architecture search. Machine Learning: Science and Technology, 2022. paper

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3. Learning operations for neural PDE solvers. ICLR, 2019. paper

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4. AutoPINN: When AutoML meets physics-informed neural networks. arXiv, 2022. paper

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5. NAS-PINN: Neural architecture search-guided physics-informed neural network for solving PDEs. arXiv, 2023. paper

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1. ADLGM: An efficient adaptive sampling deep learning Galerkin method. JCP, 2023. paper

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2. DMIS: Dynamic mesh-based importance sampling for training physics-informed neural networks. AAAI, 2023. paper

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3. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2022. paper

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4. Mitigating propagation failures in PINNs using evolutionary sampling. arXiv, 2022. paper

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5. Residual-quantile adjustment for adaptive training of physics-informed neural network. arXiv, 2022. paper

   Jiayue Han, Zhiqiang Cai, Zhiyou Wu, and Xiang Zhou.

6. Adversarial sampling for solving differential equations with neural networks. NIPS, 2021. paper

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7. A novel adaptive causal sampling method for physics-informed neural networks. arXiv, 2022. paper

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8. Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving PDEs with sharp solutions. arXiv, 2023. paper

   Zhiping Mao and Xuhui Meng.

9. Active learning based sampling for high-dimensional nonlinear partial differential equations. JCP, 2023. paper

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10. Adversarial adaptive sampling: Unify PINN and optimal yransport for the approximation of PDEs. arXiv, 2023. paper

    Kejun Tang, Jiayu Zhai, Xiaoliang Wan, and Chao Yang.

11. Coupling parameter and particle dynamics for adaptive sampling in neural Galerkin schemes. arXiv, 2023. paper

    Yuxiao Wen, Eric Vanden-Eijnden, and Benjamin Peherstorfer.

12. Mitigating propagation failures in physics-informed neural networks using retain-resample-release (R3) sampling. ICML, 2023. paper

    Arka Daw, Jie Bu, Sifan Wang, Paris Perdikaris, and Anuj Karpatne.

13. Good lattice training: Physics-informed neural networks accelerated by number theory. arXiv, 2023. paper

    Takashi Matsubara and Takaharu Yaguchi.

1. Multiscale simulations of complex systems by learning their effective dynamics. NMI, 2022. paper

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2. A latent space solver for PDE generalization. ICLR, 2021. paper

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3. Approximate latent force model inference. AAAI, 2021. paper

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4. Learning to accelerate partial differential equations via latent global evolution. NIPS, 2022. paper

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5. Exploring physical latent spaces for deep learning. arXiv, 2022. paper

   Chloe Paliard, Nils Thuerey, and Kiwon Um.

6. Certified data-driven physics-informed greedy auto-encoder simulator. arXiv, 2022. paper

   Xiaolong He, Youngsoo Choi, William D. Fries, Jonathan L. Belof, and Jiun-Shyan Chen.

7. Deep latent regularity network for modeling stochastic partial differential equations. AAAI, 2023. paper

   Shiqi Gong, Peiyan Hu, Qi Meng, Yue Wang, Rongchan Zhu, Bingguang Chen, Zhiming Ma, Hao Ni, and Tieyan Liu.

8. Learning in latent spaces improves the predictive accuracy of deep neural operators. arXiv, 2023. paper

   Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, and Michael D. Shields.

9. Solving high-dimensional PDEs with latent spectral models. ICML, 2023. paper

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1. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. JCP, 2021. paper

   Ameya D.Jagtap, KenjiKawaguchi, and George Em Karniadakis.

2. Adaptive deep neural networks methods for high-dimensional partial differential equations. JCP, 2022. paper

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3. Self-adaptive loss balanced Physics-informed neural networks. Neurocomputing, 2022. paper

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4. Multi-objective loss balancing for physics-informed deep learning. arXiv, 2021. paper

   Rafael Bischof and Michael Kraus.

5. Self-scalable Tanh (Stan): Faster convergence and better generalization in physics-informed neural networks. arXiv, 2022. paper

   Raghav Gnanasambandam, Bo Shen, Jihoon Chung, Xubo Yue, and Zhenyu (James) Kong.

6. Is L2 physics-informed loss always suitable for training physics-informed neural network? arXiv, 2022. paper

   Chuwei Wang, Shanda Li, Di He, and Liwei Wang.

7. Loss landscape engineering via data regulation on PINNs. arXiv, 2022. paper

   Vignesh Gopakumar, Stanislas Pamela, and Debasmita Samaddar.

8. Implicit stochastic gradient descent for training physics-informed neural networks. AAAI, 2023. paper

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9. About optimal loss function for training physics-informed neural networks under respecting causality. arXiv, 2023. paper

   Vasiliy A. Es'kin, Danil V. Davydov, Ekaterina D. Egorova, Alexey O. Malkhanov, Mikhail A. Akhukov, and Mikhail E. Smorkalov.

10. Learning from integral losses in physics informed neural networks. arXiv, 2023. paper

    Ehsan Saleh, Saba Ghaffari, Timothy Bretl, Luke Olson, and Matthew West.

11. A symmetry group based supervised learning method for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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1. Composing partial differential equations with physics-aware neural networks. ICLR, 2022. paper

   Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, Wolfgang Nowak, and Martin V. Butz.

2. Learning composable energy surrogates for PDE order reduction. NIPS, 2020. paper

   Alex Beatson, Jordan T. Ash, Geoffrey Roeder, Tianju Xue, and Ryan P. Adams.

3. Neural basis functions for accelerating solutions to high mach euler equations. ICML, 2022. paper

   David Witman, Alexander New, Hicham Alkandry, and Honest Mrema.

4. PFNN-2: A domain decomposed penalty-free neural network method for solving partial differential equations. arXiv, 2022. paper

   Hailong Shen and Chao Yang.

5. Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equations. arXiv, 2021. paper

   Ben Moseley, Andrew Markham, and Tarje Nissen-Meyer.

6. Finite basis physics-informed neural networks as a Schwarz domain decomposition method. arXiv, 2022. paper

   Victorita Dolean, Alexander Heinlein, Siddhartha Mishra, and Ben Moseley.

7. NeuralStagger: Accelerating physics constrained neural PDE solver with spatial-temporal decomposition. ICML, 2023. paper

   Xinquan Huang, Wenlei Shi, Qi Meng, Yue Wang, Xiaotian Gao, Jia Zhang, and Tieyan Liu.

8. Augmenting physical models with deep networksfor complex dynamics forecasting. Journal of Statistical Mechanics: Theory and Experiment, 2021. paper

   Yuan Yin, Vincent Le Guen, Jérémie Dona, Emmanuel de Bézenac, Ibrahim Ayed, Nicolas Thome, and Patrick Gallinari.

9. LordNet: Learning to solve parametric partial differential equations without simulated data. arXiv, 2022. paper

   Wenlei Shi, Xinquan Huang, Xiaotian Gao, Xinran Wei, Jia Zhang, Jiang Bian, Mao Yang, and Tieyan Liu.

10. An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations. arXiv, 2022. paper

    Ivan Prusak, Monica Nonino, Davide Torlo, Francesco Ballarin, and Gianluigi Rozza.

11. NUNO: A general gramework for learning parametric PDEs with non-uniform data. ICML, 2023. paper

    Songming Liu, Zhongkai Hao, Chengyang Ying, Hang Su, Ze Cheng, and Jun Zhu.

12. Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies. arXiv, 2023. paper

    Alena Kopaničáková, Hardik Kothari, George Em Karniadakis, and Rolf Krause.

13. Multilevel domain decomposition-based architectures for physics-informed neural networks. arXiv, 2023. paper

    Victorita Dolean, Alexander Heinlein, Siddhartha Mishra, and Ben Moseley.

14. A generalized Schwarz-type non-overlapping domain decomposition method using Physics-constrained neural networks. arXiv, 2023. paper

    Shamsulhaq Basir and Inanc Senocak.

15. Friedrichs' systems discretized with the Discontinuous Galerkin method: Domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions. arXiv, 2023. paper

    Francesco Romor, Davide Torlo, and Gianluigi Rozza.

16. A generalized Schwarz-type non-overlapping domain decomposition method using physics-constrained neural networks. arXiv, 2023. paper

    Shamsulhaq Basir and Inanc Senocak.

1. MeshingNet: A new mesh generation method based on deep learning. ICCS, 2022. paper

   Zheyan Zhang, Yongxing Wang, Peter K. Jimack, and He Wang.

2. M2N: Mesh movement networks for PDE solvers. arXiv, 2022. paper

   Wenbin Song, Mingrui Zhang, Joseph G. Wallwork, Junpeng Gao, Zheng Tian, Fanglei Sun, Matthew D. Piggott, Junqing Chen, Zuoqiang Shi, Xiang Chen, and Jun Wang.

3. RANG: A residual-based adaptive node generation method for physics-informed neural networks. arXiv, 2022. paper

   Wei Peng, Weien Zhou, Xiaoya Zhang, Wen Yao, and Zheliang Liu.

4. Learning a mesh motion technique with application to fluid-structure interaction and shape optimization. arXiv, 2022. paper

   Johannes Haubne and Miroslav Kuchta.

5. Accelerated training of physics-informed neural networks (PINNs) using meshless discretizations. arXiv, 2022. paper

   Ramansh Sharma and Varun Shankar.

6. An improved structured mesh generation method based on physics-informed neural networks. arXiv, 2022. paper

   Xinhai Chen, Jie Liu, Junjun Yan, Zhichao Wang, and Chunye Gong.

7. Mesh-free Eulerian physics-informed neural networks. arXiv, 2022. paper

   Fabricio Arend Torres, Marcello Massimo Negri, Monika Nagy-Huber, Maxim Samarin, and Volker Roth.

8. Fixed-budget online adaptive mesh learning for physics-informed neural networks. Towards parameterized problem inference. arXiv, 2022. paper

   Thi Nguyen Khoa Nguyen, Thibault Dairay, Raphaël Meunier, Christophe Millet, and Mathilde Mougeot.

9. Learning controllable adaptive simulation for multi-resolution physics. ICLR, 2023. paper

   Tailin Wu, Takashi Maruyama, Qingqing Zhao, Gordon Wetzstein, and Jure Leskovec.

10. A closest point method for surface PDEs with interior boundary conditions for geometry processing. arXiv, 2023. paper

    Nathan King, Haozhe Su, Mridul Aanjaneya, Steven Ruuth, and Christopher Batty.

11. Efficient training of physics-informed neural networks with direct grid refinement algorithm. arXiv, 2023. paper

    Shikhar Nilabh and Fidel Grandia.

1. A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks. NCS, 2021. paper

   Teeratorn Kadeethum, Daniel O’Malley, Jan Niklas Fuhg, Youngsoo Choi, Jonghyun Lee, Hari S. Viswanathan, and Nikolaos Bouklas.

2. Neural SDEs as infinite-dimensional GANs. ICML, 2021. paper

   Patrick Kidger, James Foster, Xuechen Li, and Terry J Lyons.

3. PID-GAN: A GAN framework based on a physics-informed discriminator for uncertainty quantification with physics. KDD, 2021. paper

   Arka Daw, M. Maruf, and Anuj Karpatne.

4. Generative adversarial neural operators. Transactions on Machine Learning Research, 2022. paper

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5. Weak adversarial networks for high-dimensional partial differential equations. JCP, 2020. paper

   Yaohua Zang, Gang Bao, Xiaojing Ye, and Haomin Zhou.

6. Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks. JCP, 2022. paper

   Yihang Gao and Michael K. Ng.

7. Competitive physics informed networks. ICLR, 2023. paper

   Qi Zeng, Yash Kothari, Spencer H Bryngelson, and Florian Tobias Schaefer.

8. Learning generative neural networks with physics knowledge. Research in the Mathematical Sciences, 2022. paper

   Kailai Xu, Weiqiang Zhu, and Eric Darve.

9. Diffusion generative models in infinite dimensions. arXiv, 2022. paper

   Gavin Kerrigan, Justin Ley, and Padhraic Smyth.

10. Revisiting PINNs: Generative adversarial physics-informed neural networks and point-weighting method. arXiv, 2022. paper

    Wensheng Li, Chao Zhang, Chuncheng Wang, Hanting Guan, and Dacheng Tao.

11. PIAT: Physics informed adversarial training for solving partial differential equations. arXiv, 2022. paper

    Simin Shekarpaz, Mohammad Azizmalayeri, and Mohammad Hossein Rohban.

12. Physics-constrained generative adversarial networks for 3D turbulence. arXiv, 2022. paper

    Dima Tretiak, Arvind T. Mohan, and Daniel Livescu.

13. Score-based diffusion models in function space. arXiv, 2023. paper

    Jae Hyun Lim, Nikola B. Kovachki, Ricardo Baptista, Christopher Beckham, Kamyar Azizzadenesheli, Jean Kossaifi, Vikram Voleti, Jiaming Song, Karsten Kreis, Jan Kautz, Christopher Pal, Arash Vahdat, and Anima Anandkumar.

14. Infinite-dimensional diffusion models for function spaces. arXiv, 2023. paper

    Jakiw Pidstrigach, Youssef Marzouk, Sebastian Reich, and Sven Wang.

15. A physics-informed diffusion model for high-fidelity flow field reconstruction. JCP, 2023. paper

    Dule Shu, Zijie Li, and Amir Barati Farimani.

16. Generative modelling with inverse heat dissipation. ICLR, 2023. paper

    Severi Rissanen, Markus Heinonen, and Arno Solin.

17. Differentiable Gaussianization layers for inverse problems regularized by deep generative models. ICLR, 2023. paper

    Dongzhuo Li.

18. Transformer meets boundary value inverse problems. ICLR, 2023. paper

    Ruchi Guo, Shuhao Cao, and Long Chen.

19. ViTO: Vision Transformer-operator. arXiv, 2023. paper

    Oded Ovadia, Adar Kahana, Panos Stinis, Eli Turkel, and George Em Karniadakis.

20. LatentPINNs: Generative physics-informed neural networks via a latent representation learning. arXiv, 2023. paper

    Mohammad H. Taufik and Tariq Alkhalifah.

21. Generative diffusion learning for parametric partial differential equations. arXiv, 2023. paper

    Ting Wang, Petr Plechac, and Jaroslaw Knap.

22. Scalable Transformer for PDE surrogate modeling. arXiv, 2023. paper

    Zijie Li, Dule Shu, and Amir Barati Farimani.

23. Latent traversals in generative models as potential flows. ICML, 2023. paper

    Yue Song, T. Anderson Keller, Nicu Sebe, and Max Welling.

24. Learning space-time continuous neural PDEs from partially observed states. arXiv, 2023. paper

    Valerii Iakovlev, Markus Heinonen, and Harri Lähdesmäki.

25. DiTTO: Diffusion-inspired temporal Transformer operator. arXiv, 2023. paper

    Oded Ovadia, Eli Turkel, Adar Kahana, and George Em Karniadakis.

26. PINNsFormer: A Transformer-based framework For physics-informed neural networks. arXiv, 2023. paper

    Leo Zhiyuan Zhao, Xueying Ding, and B. Aditya Prakash.

1. PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations. arXiv, 2022. paper

   Jiahao Zhang, Shiqi Zhang, and Guang Lin.

2. Solving and learning nonlinear PDEs with Gaussian processes. JCP, 2021. paper

   Yifan Chen, Bamdad Hosseini, Houman Owhadi, and Andrew M.Stuart.

3. Neural-net-induced Gaussian process regression for function approximation and PDE solution. JCP, 2019. paper

   Guofei Pang, Liu Yang, and George Em Karniadakis.

4. Learning neural optimal interpolation models and solvers. arXiv, 2022. paper

   Maxime Beauchamp, Joseph Thompson, Hugo Georgenthum, Quentin Febvre, and Ronan Fablet.

5. Inference of nonlinear partial differential equations via constrained Gaussian processes. arXiv, 2022. paper

   Zhaohui Li, Shihao Yang, and Jeff Wu.

6. Gaussian process priors for systems of linear partial differential equations with constant coefficients. arXiv, 2022. paper

   Marc Härkönen, Markus Lange-Hegermann, and Bogdan Raiţă.

7. Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes. arXiv, 2023. paper

   Yifan Chen, Houman Owhadi, and Florian Schäfer.

8. A mini-batch method for solving nonlinear PDEs with Gaussian processes. arXiv, 2023. paper

   Xianjin Yang and Houman Owhadi.

9. Random grid neural processes for parametric partial differential equations. ICML, 2023. paper

   Arnaud Vadeboncoeur, Ieva Kazlauskaite, Yanni Papandreou, Fehmi Cirak, Mark Girolami, and Omer Deniz Akyildiz.

10. Gaussian process priors for systems of linear partial differential equations with constant coefficients. ICML, 2023. paper

    Marc Harkonen, Markus Lange-Hegermann, and Bogdan Raita.

1. Solver-in-the-loop: Learning from differentiable physics to interact with iterative PDE-solvers. NIPS, 2020. paper

   Kiwon Um, Robert Brand, Yun (Raymond) Fei, Philipp Holl, and Nils Thuerey.

2. Lie point symmetry data augmentation for neural PDE solvers. ICML, 2022. paper

   Johannes Brandstetter, Max Welling, and Daniel E. Worrall.

3. Incorporating symmetry into deep dynamics models for improved generalization. ICLR, 2021. paper

   Rui Wang, Robin Walters, and Rose Yu.

4. HyperSolvers: Toward fast continuous-depth models. NIPS, 2020. paper

   Michael Poli, Stefano Massaroli, Atsushi Yamashita, Hajime Asama, and Jinkyoo Park.

5. PIXEL: Physics-informed cell representations for fast and accurate PDE solvers. NIPS, 2022. paper

   Namgyu Kang, Byeonghyeon Lee, Youngjoon Hong, Seok-Bae Yun, and Eunbyung Park.

6. NeuralSim: Augmenting differentiable simulators with neural networks. ICRA, 2021. paper

   Eric Heiden, David Millard, Erwin Coumans, Yizhou Sheng, and Gaurav S. Sukhatme.

7. DPM: A deep learning PDE augmentation method with application to large-eddy simulation. JCP, 2020. paper

   Justin Sirignano, Jonathan F.MacArt, and Jonathan B.Freund.

8. General covariance data augmentation for neural PDE solvers. ICML, 2023. paper

   Vladimir Fanaskov, Tianchi Yu, Alexander Rudikov, and Ivan Oseledets.

9. Learning preconditioners for conjugate gradient PDE solvers. ICML, 2023. paper

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10. Stability of implicit neural networks for long-term forecasting in dynamical systems. ICLR, 2023. paper

    Leon Migus, Julien Salomon, and Patrick Gallinari.

11. Training deep surrogate models with large scale online learning. ICML, 2023. paper

    Lucas Meyer, Marc Schouler, Robert A. Caulk, Alejandro Ribes, and Bruno Raffin.

12. Self-supervised learning with Lie symmetries for partial differential equations. arXiv, 2023. paper

    Grégoire Mialon, Quentin Garrido, Hannah Lawrence, Danyal Rehman, Yann LeCun, and Bobak T. Kiani.

1. PI-VAE: Physics-informed variational auto-encoder for stochastic differential equations. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   Weiheng Zhong and Hadi Meidani.

2. Robust SDE-based variational formulations for solving linear PDEs via deep learning. ICML, 2022. paper

   Lorenz Richter and Julius Berner.

3. HP-VPINNs: Variational physics-informed neural networks with domain decomposition. Computer Methods in Applied Mechanics and Engineering, 2021. paper

   Ehsan Kharazmi, Zhongqiang Zhang, and George Em Karniadakis.

4. Variational onsager neural networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs. Journal of the Mechanics and Physics of Solids, 2022. paper

   Shenglin Huang, Zequn He, Bryan Chem, and Celia Reina.

5. Solving PDEs by variational physics-informed neural networks: A posteriori error analysis. arXiv, 2022. paper

   Stefano Berrone, Claudio Canuto, and Moreno Pintore.

6. Variational Monte Carlo approach to partial differential equations with neural networks. arXiv, 2022. paper

   Moritz Reh and Martin Gärttner.

7. Energetic variational neural network discretizations to gradient flows. arXiv, 2022. paper

   Ziqing Hu, Chun Liu, Yiwei Wang, and Zhiliang Xu.

8. Variational Bayes deep operator network: A data-driven Bayesian solver for parametric differential equations. arXiv, 2022. paper

   Shailesh Garg and Souvik Chakraborty.

9. Variational inference in neural functional prior using normalizing flows: Application to differential equation and operator learning problems. arXiv, 2023. paper

   Xuhui Meng.

10. Neural network approximations of PDEs beyond linearity: A representational perspective. ICML, 2023. paper

    Tanya Marwah, Zachary Chase Lipton, Jianfeng Lu, and Andrej Risteski.

1. Bayesian deep learning for partial differential equation parameter discovery with sparse and noisy data. JCP: X, 2022. paper

   Christophe Bonneville and Christopher Earls.

2. B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. JCP, 2021. paper

   Liu Yang, Xuhui Meng, and George Em Karniadakis.

3. Approximate Bayesian neural operators: Uncertainty quantification for parametric PDEs. arXiv, 2022. paper

   Emilia Magnani, Nicholas Krämer, Runa Eschenhagen, Lorenzo Rosasco, and Philipp Hennig.

4. Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants. arXiv, 2022. paper

   L. Mars Gao and J. Nathan Kutz.

5. Bayesian physics informed neural networks for data assimilation and spatio-temporal modelling of wildfires. arXiv, 2022. paper

   Joel Janek Dabrowski, Daniel Edward Pagendam, James Hilton, Conrad Sanderson, Daniel MacKinlay, Carolyn Huston, Andrew Bolt, and Petra Kuhnert.

1. Lagrangian PINNs: A causality–conforming solution to failure modes of physics-informed neural networks. arXiv, 2022. paper

   Rambod Mojgani, Maciej Balajewicz, and Pedram Hassanzadeh.

2. AL-PINNs: Augmented Lagrangian relaxation method for physics-informed neural networks. arXiv, 2022. paper

   Hwijae Son, Sung Woong Cho, and Hyung Ju Hwang.

3. Lagrangian flow networks for conservation laws. arXiv, 2023. paper

   Fabricio Arend Torres, Marcello Massimo Negri, Marco Inversi, and Jonathan Aellen.

4. An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks. arXiv, 2023. paper

   Shamsulhaq Basir and Inanc Senocak.

5. Constrained optimization via exact augmented Lagrangian and randomized iterative sketching. ICML, 2023. paper

   Ilgee Hong, Sen Na, Michael W. Mahoney, and Mladen Kolar.

6. An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks. arXiv, 2023. paper

   Shamsulhaq Basir and Inanc Senocak.

1. Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. arXiv, 2021. paper

   Dongkun Zhang, Lu Lu, Ling Guo, and George Em Karniadakis.

2. Adversarial uncertainty quantification in physics-informed neural networks. JCP, 2021. paper

   Yibo Yang and Paris Perdikaris.

3. Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models. JCP, 2020. paper

   Ramakrishna Tipireddy, David A.Barajas-Solano, and Alexandre M.Tartakovsky.

4. Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. JCP, 2019. paper

   Yinhao Zhu, Nicholas Zabarasa, Phaedon-Stelios Koutsourelakisb, and Paris Perdikaris.

5. Error-aware B-PINNs: Improving uncertainty quantification in Bayesian physics-informed neural networks. arXiv, 2022. paper

   Olga Graf, Pablo Flores, Pavlos Protopapas, and Karim Pichara.

6. Physics-informed information field theory for modeling physical systems with uncertainty quantification. arXiv, 2023. paper

   Alex Alberts and Ilias Bilionis.

7. Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles. arXiv, 2023. paper

   Romit Maulik, Romain Egele, Krishnan Raghavan, and Prasanna Balaprakash.

8. Physics-informed variational inference for uncertainty quantification of stochastic differential equations. JCP, 2023. paper

   Hyomin Shin and Minseok Choi.

9. Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons. JCP, 2023. paper

   Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis.

1. Neural Galerkin scheme with active learning for high-dimensional evolution equations. arXiv, 2022. paper

   Joan Bruna, Benjamin Peherstorfer, and Eric Vanden-Eijnden.

2. Discovering and forecasting extreme events via active learning in neural operators. arXiv, 2022. paper

   Ethan Pickering, Stephen Guth, George Em Karniadakis, and Themistoklis P. Sapsis.

3. Active learning based sampling for high-dimensional nonlinear partial differential equations. JCP, 2023. paper

   Wenhan Gao and Chunmei Wang.

1. Hierarchical deep learning of multiscale differential equation time-steppers. Philosophical Transactions of the Royal Society A, 2022. paper

   Yuying Liu, J. Nathan Kutz, and Steven L. Brunton.

2. NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems. JCP, 2022. paper

   Wing Tat Leung, Guang Lin, and Zecheng Zhang.

3. Deep multiscale model learning. JCP, 2020. paper

   Yating Wang, Siu Wun Cheung, Eric T.Chung, Yalchin Efendiev, and Min Wang.

4. Multi-scale deep neural networks for solving high dimensional PDEs. arXiv, 2019. paper

   Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz.

5. Towards multi-spatiotemporal-scale generalized PDE modeling. arXiv, 2022. paper

   Jayesh K. Gupta and Johannes Brandstetter.

6. MultiAdam: Parameter-wise scale-invariant optimizer for multiscale training of physics-informed neural networks. ICML, 2023. paper

   Jiachen Yao, Chang Su, Zhongkai Hao, Songming Liu, Hang Su, and Jun Zhu.

7. Learning homogenization for elliptic operators. arXiv, 2023. paper

   Kaushik Bhattacharya, Nikola Kovachki, Aakila Rajan, Andrew M. Stuart, and Margaret Trautner.

1. Multifidelity deep operator networks. arXiv, 2022. paper

   Amanda A. Howard, Mauro Perego, George Em Karniadakis, and Panos Stinis.

2. Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion. JCP, 2022. paper

   Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhiqin John Xu, and Zheng Ma.

3. A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems. JCP, 2020. paper

   Xuhui Meng and George Em Karniadakis.

4. Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport. Physical Review Research, 2022. paper

   Lu Lu, Raphaël Pestourie, Steven G. Johnson, and Giuseppe Romano.

1. Learning to optimize multigrid PDE solvers. ICML, 2019. paper

   Daniel Greenfeld, Meirav Galun, Ronen Basri, Irad Yavneh, and Ron Kimmel.

2. Reducing operator complexity in algebraic multigrid with machine learning approaches. arXiv, 2023. paper

   Ru Huang, Kai Chang, Huan He, Ruipeng Li, and Yuanzhe Xi.

1. Fast PDE-constrained optimization via self-supervised operator learning. arXiv, 2021. paper

   Sifan Wang, Mohamed Aziz Bhouri, and Paris Perdikaris.

2. An extended physics informed neural network for preliminary analysis of parametric optimal control problems. arXiv, 2021. paper

   Nicola Demo, Maria Strazzullo, and Gianluigi Rozza.

3. Optimal control of PDEs using physics-informed neural networks. JCP, 2023. paper

   Saviz Mowlavi and Saleh Nabi.

4. Solving PDE-constrained control problems using operator learning. AAAI, 2022. paper

   Rakhoon Hwang, Jae Yong Lee, Jin Young Shin, and Hyung Ju Hwang.

5. PDE-based optimal strategy for unconstrained online learning. ICML, 2022. paper

   Zhiyu Zhang, Ashok Cutkosky, and Ioannis Paschalidis.

6. Control of partial differential equations via physics-informed neural networks. Journal of Optimization Theory and Applications, 2022. paper

   Carlos J. García-Cervera, Mathieu Kessler, and Francisco Periago.

7. A machine learning framework for solving high-dimensional mean field game and mean field control problems. PNAS, 2020. paper

   Lars Ruthottoa, Stanley J. Osherc, Wuchen Lic, Levon Nurbekyanc, and Samy Wu Fung.

8. Bi-level physics-informed neural networks for PDE constrained optimization using Broyden's hypergradients. ICLR, 2023. paper

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9. A combination technique for optimal control problems constrained by random PDEs. arXiv, 2022. paper

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10. A multilevel reinforcement learning framework for PDE-based control. arXiv, 2022. paper

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11. Optimal learning of high-dimensional classification problems using deep neural networks. arXiv, 2022. paper

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12. The ADMM-PINNs algorithmic framework for nonsmooth PDE-constrained optimization: A deep learning approach. arXiv, 2023. paper

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13. Learning differentiable solvers for systems with hard constraints. ICLR, 2023. paper

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14. Volumetric optimal transportation by fast Fourier transform. ICLR, 2023. paper

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15. PDE-based optimal strategy for unconstrained online learning. ICML, 2022. paper

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16. PDE-constrained models with neural network terms: Optimization and global convergence. JCP, 2023. paper

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17. Topology optimization using neural networks with conditioning field initialization for improved efficiency. arXiv, 2023. paper

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18. Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology. JCP, 2023. paper

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19. Constrained optimization via exact augmented lagrangian and randomized iterative sketching. ICML, 2023. paper

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20. Efficient PDE-constrained optimization under high-dimensional uncertainty using derivative-informed neural operators. arXiv, 2023. paper

    Dingcheng Luo, Thomas O'Leary-Roseberry, Peng Chen, and Omar Ghattas.

21. Dimension-independent certified neural network watermarks via mollifier smoothing. ICML, 2023. paper

    Jiaxiang Ren, Yang Zhou, Jiayin Jin, Lingjuan Lyu, and Da Yan.

22. Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems. arXiv, 2023. paper

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1. Physics-informed neural networks (PINNs) for fluid mechanics: A review. Acta Mechanica Sinica, 2021. paper

   Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, and George Em Karniadakis.

2. Neural operator prediction of linear instability waves in high-speed boundary layers. JCP, 2022. paper

   Patricio Clark Di Leoni, Lu Lu, Charles Meneveau, George Karniadakis, and Tamer A. Zaki.

3. A physics-informed convolutional neural network for the simulation and prediction of two-phase darcy flows in heterogeneous porous media. JCP, 2023. paper

   Zhao Zhang, Xia Yan, Piyang Liu, Kai Zhang, Renmin Han, and Sheng Wang.

4. DiscretizationNet: A machine-learning based solver for Navier–Stokes equations using finite volume discretization. Computer Methods in Applied Mechanics and Engineering, 2021. paper

   Rishikesh Ranade, Chris Hillb, and Jay Pathak.

5. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Computer Methods in Applied Mechanics and Engineering, 2020. paper

   Luning Sun, Han Gao, Shaowu Pan, and Jianxun Wang.

6. Towards physics-informed deep learning for turbulent flow prediction. KDD, 2020. paper

   Rui Wang, Karthik Kashinath, Mustafa Mustafa, Adrian Albert, and Rose Yu.

7. Learning to estimate and refine fluid motion with physical dynamics. ICML, 2022. paper

   Mingrui Zhang, Jianhong Wang, James Tlhomole, and Matthew D. Piggott.

8. Physics informed neural fields for smoke reconstruction with sparse data. ACM Transactions on Graphics, 2022. paper

   Mengyu Chu, Lingjie Liu, Quan Zheng, Erik Franz, Hans-Peter Seidel, Christian Theobalt, and Rhaleb Zayer.

9. Physics-informed deep learning for traffic state estimation: A hybrid paradigm informed by second-order traffic models. AAAI, 2021. paper

   Rongye Shi, Zhaobin Mo, and Xuan Di.

10. Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    John M.Hanna, José V.Aguado, Sebastien Comas-Cardona, Ramz Askri, and Domenico Borzacchiello.

11. Learned turbulence modelling with differentiable fluid solvers: Physics-based loss-functions and optimisation horizons. JFM, 2022. paper

    Björn List, Liwei Chen, and Nils Thuerey.

12. Learning hydrodynamic equations for active matter from particle simulations and experiments. PNAS, 2023. paper

    Rohit Supekar, Boya Song, Alasdair Hastewell, Gary P. T. Choi, Alexander Mietke, and Jörn Dunkel.

13. Physics informed neural networks: A case study for gas transport problems. JCP, 2023. paper

    Erik Laurin Strelow, Alf Gerisch, Jens Lang, and Marc E. Pfetsch.

14. Turbulence model augmented physics informed neural networks for mean flow reconstruction. arXiv, 2023. paper

    Yusuf Patel, Vincent Mons, Olivier Marquet, and Georgios Rigas.

15. RANS-PINN based simulation surrogates for predicting turbulent flows. arXiv, 2023. paper

    Shinjan Ghosh, Amit Chakraborty, Georgia Olympia Brikis, and Biswadip Dey.

16. Meta-learning for airflow simulations with graph neural networks. arXiv, 2023. paper

    Wenzhuo Liu, Mouadh Yagoubi, and Marc Schoenauer.

17. Learning operators for identifying weak solutions to the Navier-Stokes equations. arXiv, 2023. paper

    Dixi Wang and Cheng Yu.

18. Physics-informed neural networks modeling for systems with moving immersed boundaries: Application to an unsteady flow past a plunging foil. arXiv, 2023. paper

    Rahul Sundar, Dipanjan Majumdar, Didier Lucor, and Sunetra Sarkar.

19. A machine learning pressure emulator for hydrogen embrittlement. ICML, 2023. paper

    Minh Triet Chau, João Lucas de Sousa Almeida, Elie Alhajjar, and Alberto Costa Nogueira Junior.

20. A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty. arXiv, 2023. paper

    Atul Agrawal and Phaedon-Stelios Koutsourelakis.

21. Physics-informed machine learning for calibrating macroscopic traffic flow models. arXiv, 2023. paper

    Yu Tang, Li Jin, and Kaan Ozbay.

22. Radial basis function-differential quadrature-based physics-informed neural network for steady incompressible flows. Physics of Fluids, 2023. paper

    Yang Xiao, Liming Yang, Yinjie Du, Yuxin Song, and Chang Shu.

23. Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator. Physics of Fluids, 2023. paper

    Zhijie Li, Wenhui Peng, Zelong Yuan, and Jianchun Wang.

24. Physics-informed neural networks for parametric compressible Euler equations. arXiv, 2023. paper

    Simon Wassing, Stefan Langer, and Philipp Bekemeyer.

25. Simulation of rarefied gas flows using physics-informed neural network combined with discrete velocity method. Physics of Fluids, 2023. paper

    Linying Zhang, Wenjun Ma, Qin Lou, and Jun Zhang.

1. Occupancy networks: Learning 3D reconstruction in function space. CVPR, 2019. paper

   Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger.

2. Transfer learning for flow reconstruction based on multifidelity data. AIAA Journal, 2022. paper

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3. Learning-based state reconstruction for a scalar hyperbolic PDE under noisy lagrangian sensing. L4DC, 2022. paper

   Matthieu Barreau, John Liu, and Karl Henrik Johansson.

1. Dynamic weights enabled physics-informed neural network for simulating the mobility of engineered nano-particles in a contaminated aquifer. NIPS, 2022. paper

   Shikhar Nilabh and Fidel Grandia.

2. Learning two-phase microstructure evolution using neural operators and autoencoder architectures. NPJ Computational Materials, 2022. paper

   Vivek Oommen, Khemraj Shukla, Somdatta Goswami, Rémi Dingreville, and George Em Karniadakis.

3. Predicting glass structure by physics-informed machine learning. NPJ Computational Materials, 2022. paper

   Mikkel L. Bødker, Mathieu Bauchy, Tao Du, John C. Mauro, and Morten M. Smedskjaer.

4. Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium. NPJ Computational Materials, 2022. paper

   Ruiyang Li, Jianxun Wang, Eungkyu Lee, and Tengfei Luo.

5. Design of Turing systems with physics-informed neural networks. arXiv, 2022. paper

   Jordon Kho, Winston Koh, Jian Cheng Wong, Pao-Hsiung Chiu, and Chin Chun Ooi.

6. Spatio-temporal super-resolution of dynamical systems using physics-informed deep-learning. AAAI, 2023. paper

   Rajat Arora and Ankit Shrivastava.

7. Rapid seismic waveform modeling and inversion with neural operators. TGRS, 2023. paper

   Yan Yang, Angela F. Gao, Kamyar Azizzadenesheli, Robert W. Clayton, and Zachary E. Ross.

1. Learning to diffuse: A new perspective to design PDEs for visual analysis. TPAMI, 2016. paper

   Risheng Liu, Guangyu Zhong, Junjie Cao, Zhouchen Lin, Shiguang Shan, and Zhongxuan Luo.

2. Reformulating optical flow to solve image-based inverse problems and quantify uncertainty. TPAMI, 2022. paper

   Aleix Boquet-Pujadas and Jean-Christophe Olivo-Marin.

3. WarpPINN: Cine-MR image registration with physics-informed neural networks. arXiv, 2022. paper

   Pablo Arratia Lopez, Hernan Mella, Sergio Uribe, Daniel E. Hurtado, and Francisco Sahli Costabal.

4. NODE-ImgNet: A PDE-informed effective and robust model for image denoising. arXiv, 2023. paper

   Xinheng Xie, Yue Wu, Hao Nib, and Cuiyu He.

5. Microscopy image reconstruction with physics-informed denoising diffusion probabilistic model. arXiv, 2023. paper

   Rui Li, Gabriel della Maggiora, Vardan Andriasyan, Anthony Petkidis, Artsemi Yushkevich, Mikhail Kudryashev, and Artur Yakimovich.

1. Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   Tapas Tripura and Souvik Chakraborty.

2. Graph neural networks for airfoil design. arXiv, 2023. paper

   Florent Bonnet.

3. Exact Dirichlet boundary physics-informed neural network EPINN for solid mechanics. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Jiaji Wang, Y.L. Mo, Bassam Izzuddin, and Chul-Woo Kim.

4. Solving multi-material problems in solid mechanics using physics-informed neural networks based on domain decomposition technology. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Yu Diao, Jianchuan Yang, Ying Zhang, Dawei Zhang, and Yiming Du.

1. Hybrid learning of time-series inverse dynamics models for locally isotropic robot motion. RAL, 2022. paper

   Tolga-Can Çallar and Sven Böttger.

2. NTFields: Neural time fields for physics-informed robot motion planning. ICLR, 2023. paper

   Ruiqi Ni and Ahmed H Qureshi.

3. Online parameter estimation using physics-informed deep learning for vehicle stability algorithms. arXiv, 2023. paper

   Kemal Koysuren, Ahmet Faruk Keles, and Melih Cakmakci.

1. Machine learning accelerated PDE backstepping observers. arXiv, 2022. paper

   Yuanyuan Shi, Zongyi Li, Huan Yu, Drew Steeves, Anima Anandkumar, and Miroslav Krstic.

2. Neural solvers for fast and accurate numerical optimal control. NIPS, 2021. paper

   Federico Berto, Stefano Massaroli, Michael Poli, and Jinkyoo Park.

3. Bellman neural networks for the class of optimal control problems with integral quadratic cost. TAI, 2022. paper

   Enrico Schiassi, Andrea D'Ambrosio, and Roberto Furfaro.

4. Offline supervised learning vs online direct policy optimization: A comparative study and a unifie training paradigm for neural network-based optimal feedback control. arXiv, 2022. paper

   Yue Zhao and Jiequn Han.

5. Policy evaluation and temporal–difference learning in continuous time and space: A martingale approach. JMLR, 2022. paper

   Yanwei Jia and Xunyu Zhou.

6. Physics-informed kernel embeddings: Integrating prior system knowledge with data-driven control. arXiv, 2023. paper

   Adam J. Thorpe, Cyrus Neary, Franck Djeumou, Meeko M. K. Oishi, and Ufuk Topcu.

7. Distributed control of partial differential equations using convolutional reinforcement learning. arXiv, 2023. paper

   Sebastian Peitz, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, and Kunihiko Taira.

8. Neural control of parametric solutions for high-dimensional evolution PDEs. arXiv, 2023. paper

   Nathan Gaby, Xiaojing Ye, and Haomin Zhou.

9. Bridging physics-informed neural networks with reinforcement learning: Hamilton-Jacobi-Bellman proximal policy optimization (HJBPPO). arXiv, 2023. paper

   Amartya Mukherjee and Jun Liu.

10. AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems. arXiv, 2023. paper

    Pengfei Yin, Guangqiang Xiao, Kejun Tang, and Chao Yang.

11. Neural operators for bypassing gain and control computations in PDE backstepping. arXiv, 2023. paper

    Luke Bhan, Yuanyuan Shi, and Miroslav Krstic.

12. Neural operators of backstepping controller and observer gain functions for reaction-diffusion PDEs. arXiv, 2023. paper

    Miroslav Krstic, Luke Bhan, and Yuanyuan Shi.

13. Leveraging multi-time Hamilton-Jacobi PDEs for certain scientific machine learning problems. arXiv, 2023. paper

    Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, and George Em Karniadakis.

14. Learning to control PDEs with differentiable physics. ICLR, 2020. paper

    Philipp Holl, Nils Thuerey, and Vladlen Koltun.

15. A generalizable physics-informed learning framework for risk probability estimation. L4DC, 2020. paper

    Zhuoyuan Wang and Yorie Nakahira.

16. Operator learning for nonlinear adaptive control. L4DC, 2023. paper

    Luke Bhan, Yuanyuan Shi and Miroslav Krstic.

17. Optimal temperature trajectory for tubular reactor using physics informed neural networks. JCP, 2023. paper

    Rahul Patel, Sharad Bhartiya, and Ravindra Gudi.

18. Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. Journal of Process Control, 2023. paper

    Yingzhe Zheng, Cheng Hu, Xiaonan Wang, and Zhe Wu.

19. **Physics-guided neural networks for inversion-based feedforward control applied to hybrid stepper motors.**arXiv, 2023. paper

    Daiwei Fan, Max Bolderman, Sjirk Koekebakker, Hans Butler, and Mircea Lazar.

20. Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. JCP, 2023. paper

    Yingzhe Zheng, Cheng Hu, Xiaonan Wang, and Zhe Wu.

21. Optimal Dirichlet boundary control by Fourier neural operators applied to nonlinear optics. arXiv, 2023. paper

    Nils Margenberg, Franz X. Kärtner, and Markus Bause.

22. Neural operators for delay-compensating control of hyperbolic PIDEs. arXiv, 2023. paper

    Jie Qi, Jing Zhang, and Miroslav Krstic.

23. Physics-informed online learning of gray-box models by moving horizon estimation. European Journal of Control, 2023. paper

    Kristoffer Fink Løwenstein, Daniele Bernardini, Lorenzo Fagiano, and Alberto Bemporad.

24. Online identification and control of PDEs via reinforcement learning methods. arXiv, 2023. paper

    Alessandro Alla, Agnese Pacifico, Michele Palladino, and Andrea Pesare.

25. The hard-constraint PINNs for interface optimal control problems. arXiv, 2023. paper

    Ming-Chih Lai, Yongcun Song, Xiaoming Yuan, Hangrui Yue, and Tianyou Zeng.

1. DPM: Physics-informed Karhunen-Loéve and neural network approximations for solving inverse differential equation problems. AAAI, 2021. paper

   Jungeun Kim, Kookjin Lee, Dongeun Lee, Sheo Yon Jin, and Noseong Park.

2. Neural inverse operators for Solving PDE inverse problems. ICML, 2023. paper

   Roberto Molinaro, Yunan Yang, Björn Engquist, and Siddhartha Mishra.

3. Physics-informed Karhunen-Loéve and neural network approximations for solving inverse differential equation problems. JCP, 2022. paper

   Jing Li and Alexandre M.Tartakovsky.

4. Solving inverse problems in stochastic models using deep neural networks and adversarial training. Computer Methods in Applied Mechanics and Engineering, 2021. paper

   Kailai Xu and Eric Darve.

5. Physics-informed neural networks with hard constraints for inverse design. SIAM Journal on Scientific Computing, 2021. paper

   Lu Lu, Raphaël Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, and Steven G. Johnson.

6. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. JCP, 2019. paper

   M.Raissia, P.Perdikarisb, and George Em Karniadakis.

7. GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning. arXiv, 2023. paper

   Siddharth Nair, Timothy F. Walsh, Greg Pickrell, and Fabio Semperlotti.

8. Bayesian inversion with neural operator (BINO) for modeling subdiffusion: Forward and inverse problems. arXiv, 2022. paper

   Xiongbin Yan, Zhiqin John Xu, and Zheng Ma.

9. Maximum-likelihood estimators in physics-informed neural networks for high-dimensional inverse problems. arXiv, 2023. paper

   Gabriel S. Gusmão and Andrew J. Medford.

10. Solution of physics-based inverse problems using conditional generative adversarial networks with full gradient penalty. arXiv, 2023. paper

    Deep Ray, Javier Murgoitio-Esandi, Agnimitra Dasgupta, and Assad A. Oberai.

11. Entropy structure informed learning for inverse XDE problems. arXiv, 2023. paper

    Yan Jiang, Wuyue Yang, Yi Zhu, and Liu Hong.

12. Solving multiphysics-based inverse problems with learned surrogates and constraints. arXiv, 2023. paper

    Ziyi Yin, Rafael Orozco, Mathias Louboutin, and Felix J. Herrmann.

13. Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations. JCP, 2023. paper

    Zhiyong Zhang , Hui Zhang , Lisheng Zhang, and Leilei Guo.

1. Physics-informed neural networks for quantum eigenvalue problems. IJCNN, 2022. paper

   Henry Jin, Marios Mattheakis, and Pavlos Protopapas.

2. Quantum-inspired tensor neural networks for partial differential equations. arXiv, 2022. paper

   Raj Patel, Chia-Wei Hsing, Serkan Sahin, Saeed S. Jahromi, Samuel Palmer, Shivam Sharma, Christophe Michel, Vincent Porte, Mustafa Abid, Stephane Aubert, Pierre Castellani, Chi-Guhn Lee, Samuel Mugel, and Roman Orus.

3. Quantum Fourier networks for solving parametric PDEs. arXiv, 2023. paper

   Nishant Jain, Jonas Landman, Natansh Mathur, and Iordanis Kerenidis.

4. Q-Flow: Generative modeling for differential equations of open quantum dynamics with normalizing flows. ICML, 2023. paper

   Owen M Dugan, Peter Y. Lu, Rumen Dangovski, Di Luo, and Marin Soljacic.

5. Physics-Informed Quantum Machine Learning: Solving nonlinear differential equations in latent spaces without costly grid evaluations. arXiv, 2023. paper

   Annie E. Paine, Vincent E. Elfving, and Oleksandr Kyriienko.

1. FourCastNet: A global data-driven high-resolution weather model using adaptive Fourier neural operators. arXiv, 2022. paper

   Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, Pedram Hassanzadeh, Karthik Kashinath, and Animashree Anandkumar.

2. Fourier neural operators for arbitrary resolution climate data downscaling. JMLR, 2023. paper

   Qidong Yang, Alex Hernandez-Garcia, Paula Harder, Venkatesh Ramesh, Prasanna Sattegeri, Daniela Szwarcman, Campbell D. Watson, and David Rolnick.

3. Modelling atmospheric dynamics with spherical Fourier neural operators. ICLR, 2023. paper

   Boris Bonev, Thorsten Kurth, Christian Hundt, Jaideep Pathak, Maximilian Baust, Karthik Kashinath, and Anima Anandkumar.

4. Spatiotemporal modeling of European paleoclimate using doubly sparse Gaussian processes. NIPS, 2022. paper

   Seth D. Axen, Alexandra Gessner, Christian Sommer, Nils Weitzel, and Álvaro Tejero-Cantero.

5. ClimSim: An open large-scale dataset for training high-resolution physics emulators in hybrid multi-scale climate simulators. arXiv, 2023. paper

   Sungduk Yu, Walter M. Hannah, Liran Peng, Mohamed Aziz Bhouri, Ritwik Gupta, Jerry Lin, Björn Lütjens, Justus C. Will, Tom Beucler, Bryce E. Harrop, Benjamin R. Hillman, Andrea M. Jenney, Savannah L. Ferretti, Nana Liu, Anima Anandkumar, Noah D. Brenowitz, Veronika Eyring, Pierre Gentine, Stephan Mandt, Jaideep Pathak, Carl Vondrick, Rose Yu, Laure Zanna, Ryan P. Abernathey, Fiaz Ahmed, David C. Bader, Pierre Baldi, Elizabeth A. Barnes, Gunnar Behrens, Christopher S. Bretherton, Julius J. M. Busecke, Peter M. Caldwell, Wayne Chuang, Yilun Han, Yu Huang, Fernando Iglesias-Suarez, Sanket Jantre, Karthik Kashinath, Marat Khairoutdinov, Thorsten Kurth, Nicholas J. Lutsko, Po-Lun Ma, Griffin Mooers, J. David Neelin, David A. Randall, Sara Shamekh, Akshay Subramaniam, Mark A. Taylor, Nathan M. Urban, Janni Yuval, Guang J. Zhang, Tian Zheng, and Michael S. Pritchard.

1. Approximating discontinuous Nash equilibria values of two-player general-sum differential games. arXiv, 2022. paper

   Lei Zhang, Mukesh Ghimire, Wenlong Zhang, Zhe Xu, and Yi Ren.

1. Physics-aware machine learning surrogates for real-time manufacturing digital twin. Manufacturing Letters, 2022. paper

   Aditya Balu, Soumik Sarkar, Baskar Ganapathysubramanian, and Adarsh Krishnamurthy.

2. Multi-scale digital twin: Developing a fast and physics-informed surrogate model for groundwater contamination with uncertain climate models. arXiv, 2022. paper

   Lijing Wang, Takuya Kurihana, Aurelien Meray, Ilijana Mastilovic, Satyarth Praveen, Zexuan Xu, Milad Memarzadeh, Alexander Lavin, and Haruko Wainwright.

3. SciAI4Industry--Solving PDEs for industry-scale problems with deep learning. arXiv, 2022. paper

   Philipp A. Witte, Russell J. Hewett, Kumar Saurabh, AmirHossein Sojoodi, and Ranveer Chandra.

4. Operator learning framework for digital twin and complex engineering systems. arXiv, 2023. paper

   Kazuma Kobayashi, James Daniell, and Syed B. Alam.

1. Symmetry-informed geometric representation for molecules, proteins, and crystalline materials. arXiv, 2023. paper

   Shengchao Liu, Weitao Du, Yanjing Li, Zhuoxinran Li, Zhiling Zheng, Chenru Duan, Zhiming Ma, Omar Yaghi, Anima Anandkumar, Christian Borgs, Jennifer Chayes, Hongyu Guo, and Jian Tang.