We will revisit classical scientific computing from a statistical learning viewpoint. In this new computing paradigm, differential equations, conservation laws, and data act as complementary agents in a predictive modeling pipeline. This course aims explore the potential of modern machine learning as a unifying computational tool that enables learning models from experimental data, inferring solutions to differential equations, blending information from a hierarchy of models, quantifying uncertainty in computations, and efficiently optimizing complex engineering systems.

Specific topics to be covered span recent developments in supervised and unsupervised learning: nonlinear regression/classification with deep neural networks, multi-fidelity modeling and computation under uncertainty using Gaussian processes, Bayesian optimization, convolutional and recurrent neural networks, model reduction using principal component analysis, variational auto-encoders, and probabilistic latent variable models. The effectiveness of these tools will be demonstrated through several engineering applications including examples in fluid dynamics, heat transfer, design optimization, and modeling of cardiovascular flows.

• Basic Calculus and Linear Algebra (MATH 240 or MATH 513 or ENM 240)
• Basic Statistics and Probability (MATH 430 or ENM 321 or ENM 503)
• Scientific computing in Python and MATLAB

• MATLAB (see here for an installation guide)
• A Python enviroment set up for scientific computing (I recommend the Anaconda distribution)
• Machine learning libraries: Tensorflow, PyTorch

Students will leave this course with experience in:

• Analyzing and synthesizing data towards enhancing their understanding and ability to model physical, biological, and engineering systems.
• Hands-on skills on a broad class of machine learning tools enabling them to construct structured prediction models, propagate and quantify uncertainty, perform sensitivity analysis, and optimize systems of realistic complexity.
• Applications of these tools spanning a diverse set of engineering disciplines, including fluid dynamics, heat transfer, mechanical design, and biomedical engineering.

Paris Perdikaris is an Assistant Professor of Mechanical Engineering and Applied Mechanics. His work spans a wide range of areas in computational science and engineering, with a particular focus on the analysis and design of complex physical and biological systems using machine learning, stochastic modeling, computational mechanics, and high-performance computing. Prior to Penn, he spent two years as a post-doctoral researcher at MIT developing machine learning algorithms that synergistically combine multi-fidelity data with prior knowledge (e.g. differential equations and the conservation laws of mathematical physics) towards establishing a new paradigm in predictive modeling and decision making under uncertainty.

TAs work one-on-one with students to guide them on projects and help problem-solve. Students are advised to consult a TA if they have tried something themselves and it hasn’t worked to their satisfaction.

TA: Chenchen Hu, Office Hours: Thursdays, 1:30-3:30pm, room 401B (3401 Walnut Street, 4th floor), Email: [email protected]

This syllabus is a work in progress. The lesson plan is subject to change depending on the progress and success of the students in the class. Any changes will be notified to students.