PDE: Partial Differentiable Equation
Contributed by Chunyang Zhang.
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Physics-informed machine learning. Nature Reviews Physics, 2021. paper
George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.
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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.
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Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework. Physical Review Fluids, 2018. paper
Jinlong Wu, Heng Xiao, and Eric Paterson.
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Integrating scientific knowledge with machine learning for engineering and environmental systems. ACM Computing Surveys, 2023. paper
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Physical laws meet machine intelligence: Current developments and future directions. Artificial Intelligence Review, 2022. paper
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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.
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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
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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.
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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.
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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.
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An overview on deep learning-based approximation methods for partial differential equations. arXiv, 2020. paper
Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, and Benno Kuckuck.
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Three ways to solve partial differential equations with neural networks—A review. GAMM‐Mitteilungen, 2021. paper
Jan Blechschmidt and Oliver G. Ernst.
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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.
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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.
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Partial differential equations meet deep neural networks: A survey. arXiv, 2022. paper
Shudong Huang, Wentao Feng, Chenwei Tang, and Jiancheng Lv.
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Solving differential equations with Deep Learning: A beginner's guide. arXiv, 2023. paper
Luis Medrano Navarro, Luis Martín Moreno, and Sergio G Rodrigo.
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Deep learning algorithms for solving differential equations: a survey. Journal of Experimental & Theoretical Artificial Intelligence, 2023. paper
Harender Kumara and Neha Yadav.
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An expert's guide to training physics-informed neural networks. arXiv, 2023. paper
Sifan Wang, Shyam Sankaran, Hanwen Wang, and Paris Perdikaris.
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A survey on physics informed reinforcement learning: Review and open problems. arXiv, 2023. paper
Chayan Banerjee, Kien Nguyen, Clinton Fookes, and Maziar Raissi.
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Neural operators for accelerating scientific simulations and design. arXiv, 2023. paper
Kamyar Azzizadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, and Anima Anandkumar.
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 2020. paper
Raissi Maziar, Alireza Yazdani, and George Em Karniadakis.
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Deep hidden physics models: Deep learning of nonlinear partial differential equations. JMLR, 2018. paper
Maziar Raissi.
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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.
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Parallel physics-informed neural networks via domain decomposition. JCP, 2021. paper
Khemraj Shukla, Ameya D.Jagtap, and George Em Karniadakis.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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Physics-augmented learning: A new paradigm beyond physics-informed learning. NIPS, 2021. paper
Ziming Liu, Yuanqi Du, Yunyue Chen, and Max Tegmark.
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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.
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Solving Benjamin–Ono equation via gradient balanced PINNs approach. The European Physical Journal Plus, 2022. paper
Xiangyu Yang and Zhen Wang.
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Robust learning of physics informed neural networks. arXiv, 2021. paper
Chandrajit Bajaj, Luke McLennan, Timothy Andeen, and Avik Roy.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Anisotropic, sparse and interpretable physics-informed neural networks for PDEs. arXiv, 2022. paper
Amuthan A. Ramabathiran and Prabhu Ramachandran.
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Fast neural network based solving of partial differential equations. arXiv, 2022. paper
Jaroslaw Rzepecki, Daniel Bates, and Chris Doran.
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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.
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Learning differentiable solvers for systems with hard constraints. arXiv, 2022. paper
Geoffrey Négiar, Michael W. Mahoney, and Aditi S. Krishnapriyan.
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Momentum diminishes the effect of spectral bias in physics-informed neural networks. arXiv, 2022. paper
Ghazal Farhani, Alexander Kazachek, and Boyu Wang.
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Δ-PINNs: Physics-informed neural networks on complex geometries. arXiv, 2022. paper
Francisco Sahli Costabal, Simone Pezzuto, and Paris Perdikaris.
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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.
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FO-PINNs: A first-order formulation for physics informed neural networks. arXiv, 2022. paper
Rini J. Gladstone, Mohammad A. Nabian, and Hadi Meidani.
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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.
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Physics-informed neural networks for operator equations with stochastic data. arXiv, 2022. paper
Paul Escapil-Inchauspé and Gonzalo A. Ruz.
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Physics-informed neural networks with unknown measurement noise. arXiv, 2022. paper
Philipp Pilar and Niklas Wahlstrom.
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On the compatibility between a neural network and a partial differential equation for physics-informed learning. arXiv, 2022. paper
Kuangdai Leng and Jeyan Thiyagalingam.
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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.
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L-HYDRA: Multi-head physics-informed neural networks. arXiv, 2023. paper
Zongren Zou and George Em Karniadakis.
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PINN for dynamical partial differential equations is not training deeper networks rather learning advection and time variance. arXiv, 2023. paper
Siddharth Rout.
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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.
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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.
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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.
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Efficient physics-informed neural networks using hash encoding. arXiv, 2023. paper
Xinquan Huang and Tariq Alkhalifah.
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Ensemble learning for physics informed neural networks: A gradient boosting approach. arXiv, 2023. paper
Zhiwei Fang, Sifan Wang, and Paris Perdikaris.
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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.
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Achieving high accuracy with PINNs via energy natural gradients. arXiv, 2023. paper
Johannes Müller and Marius Zeinhofer.
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Implicit stochastic gradient descent for training physics-informed neural networks. arXiv, 2023. paper
Ye Li, Songcan Chen, and Shengjun Huang.
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NSGA-PINN: A multi-objective optimization method for physics-informed neural network training. arXiv, 2023. paper
Binghang Lu, Christian B. Moya, and Guang Lin.
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Improving physics-informed neural networks with meta-learned optimization. arXiv, 2023. paper
Alex Bihlo.
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MetaPhysiCa: OOD robustness in physics-informed machine learning. arXiv, 2023. paper
S Chandra Mouli, Muhammad Ashraful Alam, and Bruno Ribeiro.
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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.
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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.
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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.
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Provably correct physics-informed neural networks. arXiv, 2023. paper
Deqing Jiang, Justin Sirignano, and Samuel N. Cohen.
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Predictive limitations of physics-informed neural networks in vortex shedding. arXiv, 2023. paper
Pi-Yueh Chuang and Lorena A. Barba.
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Residual-based error bound for physics-informed neural networks. arXiv, 2023. paper
Shuheng Liu, Xiyue Huang, and Pavlos Protopapas.
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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.
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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.
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Separable physics informed neural networks. arXiv, 2023. paper
Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park.
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Achieving high accuracy with PINNs via energy natural gradient descent. ICML, 2023. paper
Johannes Müller and Marius Zeinhofer.
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Gradient descent finds the global optima of two-layer physics-informed neural networks. ICML, 2023. paper
Yihang Gao, Yiqi Gu, and Michael Ng.
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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.
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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.
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Tackling the curse of dimensionality with physics-informed neural networks. arXiv, 2023. paper
Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, and Kenji Kawaguchi.
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Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper
Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.
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Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper
Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.
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Tensor-compressed back-propagation-free training for (physics-informed) neural networks. arXiv, 2023. paper
Yequan Zhao, Xinling Yu, Zhixiong Chen, Ziyue Liu, Sijia Liu, and Zheng Zhang.
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How to select physics-informed neural networks in the absence of ground truth: A pareto front-based strategy. ICML, 2023. paper
Zhao Wei, Jian Cheng Wong, Nicholas Wei Yong Sung, Abhishek Gupta, Chin Chun Ooi, Pao-Hsiung Chiu, My Ha Dao, and Yew-Soon Ong.
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A gradient-enhanced physics-informed neural network (gPINN) scheme for the coupled non-fickian/non-fourierian diffusion-thermoelasticity analysis: A novel gPINN structure. Engineering Applications of Artificial Intelligence, 2023. paper
Katayoun Eshkofti and Seyed Mahmoud Hosseini.
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Learning only on boundaries: A physics-informed neural operator for solving parametric partial differential equations in complex geometries. arXiv, 2023. paper
Zhiwei Fang, Sifan Wang, and Paris Perdikaris.
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Exact and soft boundary conditions in physics-informed neural networks for the variable coefficient poisson equation. arXiv, 2023. paper
Sebastian Barschkis.
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Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms. JCP, 2023. paper
Yanxia Qian, Yongchao Zhang, Yunqing Huang, and Suchuan Dong.
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Investigating the ability of PINNs to solve burgers’ PDE near finite-time blowup. arXiv, 2023. paper
Dibyakanti Kumar and Anirbit Mukherjee.
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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.
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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. SA, 2021. paper
Wang Sifan, Hanwen Wang, and Paris Perdikaris.
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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.
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Variable-input deep operator networks. arXiv, 2022. paper
Michael Prasthofer, Tim De Ryck, and Siddhartha Mishra.
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MIONet: Learning multiple-input operators via tensor product. arXiv, 2022. paper
Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.
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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.
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Long-time integration of parametric evolution equations with physics-informed DeepONets. arXiv, 2021. paper
Sifan Wang and Paris Perdikaris.
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Improved architectures and training algorithms for deep operator networks. Journal of Scientific Computing, 2022. paper
Sifan Wang, Hanwen Wang, and Paris Perdikaris.
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SVD perspectives for augmenting DeepONet flexibility and interpretability. arXiv, 2022. paper
Simone Venturi and Tiernan Casey.
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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.
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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.
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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.
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Transfer learning enhanced DeepONet for long-time prediction of evolution equations. arXiv, 2022. paper
Wuzhe Xu, Yulong Lu, and Li Wang.
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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.
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VB-DeepONet: A Bayesian operator learning framework for uncertainty quantification. Engineering Applications of Artificial Intelligence, 2023. paper
Shailesh Garg and Souvik Chakraborty.
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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.
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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.
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A hybrid decoder-DeepONet operator regression framework for unaligned observation data. arXiv, 2023. paper
Bo Chen, Chenyu Wang, Weipeng Li, and Haiyang Fu.
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Improving physics-informed DeepONets with hard constraints. arXiv, 2023. paper
Rüdiger Brecht, Dmytro R. Popovych, Alex Bihlo, and Roman O. Popovych.
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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.
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On universal approximation and error bounds for Fourier neural operators. JMLR, 2021. paper
Nikola Kovachki, Samuel Lanthaler, and Siddhartha Mishra.
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HyperFNO: Improving the generalization behavior of Fourier neural operators. NIPS, 2022. paper
Francesco Alesiani, Makoto Takamoto, and Mathias Niepert.
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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.
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Fourier neural operator with learned deformations for PDEs on general geometries. arXiv, 2022. paper
Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, and Anima Anandkumar.
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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.
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Fast sampling of diffusion models via operator learning. NIPS, 2022. paper
Hongkai Zheng, Weili Nie, Arash Vahdat, Kamyar Azizzadenesheli, and Anima Anandkumar.
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Factorized Fourier neural operators. ICLR, 2023. paper
Alasdair Tran, Alexander Mathews, Lexing Xie, and Cheng Soon Ong.
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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.
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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.
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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.
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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.
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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.
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Incremental spectral learning Fourier neural operator. arXiv, 2022. paper
Jiawei Zhao, Robert Joseph George, Yifei Zhang, Zongyi Li, and Anima Anandkumar.
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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.
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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.
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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.
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Domain agnostic Fourier neural operators. arXiv, 2023. paper
Ning Liu, Siavash Jafarzadeh, and Yue Yu.
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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.
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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.
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Speeding up Fourier neural operators via mixed precision. arXiv, 2023. paper
Colin White, Renbo Tu, Jean Kossaifi, Gennady Pekhimenko, Kamyar Azizzadenesheli, and Anima Anandkumar.
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Geometry-informed neural operator for large-scale 3d PDEs. arXiv, 2023. paper
Zongyi Li, Nikola Borislavov Kovachki, Chris Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, and Anima Anandkumar.
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Message passing neural PDE solvers. ICLR, 2022. paper
Johannes Brandstetter, Daniel E. Worrall, and Max Welling.
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Predicting physics in mesh-reduced space with temporal attention. ICLR, 2022. paper
Xu Han, Han Gao, Tobias Pfaff, Jianxun Wang, and Liping Liu.
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Learning mesh-based simulation with graph networks. ICLR, 2021. paper
Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter Battaglia.
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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.
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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.
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Learning the solution operator of boundary value problems using graph neural networks. ICML, 2022. paper
Winfried Lötzsch, Simon Ohler, and Johannes S. Otterbach.
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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.
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Modular flows: Differential molecular generation. NIPS, 2022. paper
Yogesh Verma, Samuel Kaski, Markus Heinonen, and Vikas Garg.
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Learning to solve PDE-constrained inverse problems with graph networks. ICML, 2022. paper
Zhao Qingqing, David B. Lindell, and Gordon Wetzstein.
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A machine learning pressure emulator for hydrogen embrittlement. ICML, 2023. paper
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Towards real-time training of physics-informed neural networks: Applications in ultrafast ultrasound blood flow imaging. arXiv, 2023. paper
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Physics-informed kernel embeddings: Integrating prior system knowledge with data-driven control. arXiv, 2023. paper
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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
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Online parameter estimation using physics-informed deep learning for vehicle stability algorithms. arXiv, 2023. paper
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A locality-based neural solver for optical motion capture. SIGGRAPH, 2023. paper
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Approximating high-dimensional minimal surfaces with physics-informed neural networks. arXiv, 2023. paper
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A spatial-temporally adaptive PINN framework for 3D bi-ventricular electrophysiological simulations and parameter inference. MICCAI, 2023. paper
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Dynamic weights enabled physics-informed neural network for simulating the mobility of engineered nano-particles in a contaminated aquifer. NIPS, 2022. paper
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Design of Turing systems with physics-informed neural networks. arXiv, 2022. paper
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WarpPINN: Cine-MR image registration with physics-informed neural networks. arXiv, 2022. paper
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NODE-ImgNet: A PDE-informed effective and robust model for image denoising. arXiv, 2023. paper
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Quantum-inspired tensor neural networks for partial differential equations. arXiv, 2022. paper
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Quantum Fourier networks for solving parametric PDEs. arXiv, 2023. paper
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SciAI4Industry--Solving PDEs for industry-scale problems with deep learning. arXiv, 2022. paper
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Operator learning framework for digital twin and complex engineering systems. arXiv, 2023. paper
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Towards solving industry-grade surrogate modeling problems using physics informed machine learning. arXiv, 2023. paper
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