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ETH Zürich Deep Learning in Scientific Computing 2023
Lecture 6: Physics-Informed Neural Networks - Limitations and Extensions

Lecturers: Ben Moseley and Siddhartha Mishra

▬ Lecture Content ▬▬▬▬▬▬▬▬▬
0:00 - Recap: applications of physics-informed neural networks (PINNs)
5:52 - Lecture overview
6:44 - Limitations of PINNs
8:39 - Computational cost
11:25 - Competing loss terms
16:40 - Scaling to complex problems
26:07 - PINN research landscape
28:08 - Conditioned PINNs
38:30 - Discretised PINNs
53:17 - Training with finite differences
55:19 - [break - please skip]
1:02:53 - Using hard constraints for PINNs
1:09:52 - Adaptive loss terms
1:13:52 - Adaptive collocation points
1:18:30 - Combining PINNs with domain decomposition
1:35:44 - Summary of PINN extensions

▬ Course Overview ▬▬▬▬▬▬▬▬▬
Lecture 1: Course Introduction    • ETH Zürich DLSC: Course Introduction  
Lecture 2: Introduction to Deep Learning Part 1    • ETH Zürich DLSC: Introduction to Deep...  
Lecture 3: Introduction to Deep Learning Part 2    • ETH Zürich DLSC: Introduction to Deep...  
Lecture 4: Physics-Informed Neural Networks - Introduction    • ETH Zürich DLSC: Physics-Informed Neu...  
Lecture 5: Physics-Informed Neural Networks - Applications    • ETH Zürich DLSC: Physics-Informed Neu...  
Lecture 6: Physics-Informed Neural Networks - Limitations and Extensions    • ETH Zürich DLSC: Physics-Informed Neu...  
Lecture 7: Introduction to Operator Learning Part 1    • ETH Zürich DLSC: Introduction to Oper...  
Lecture 8: Introduction to Operator Learning Part 2    • ETH Zürich DLSC: Introduction to Oper...  
Lecture 9: Deep Operator Networks    • ETH Zürich DLSC: Deep Operator Networks  
Lecture 10: Neural Operators    • ETH Zürich DLSC: Neural Operators  
Lecture 11: Fourier Neural Operators and Convolutional Neural Operators    • ETH Zürich DLSC: Fourier Neural Opera...  
Lecture 12: Introduction to Differentiable Physics Part 1    • ETH Zürich DLSC: Introduction to Diff...  
Lecture 13: Introduction to Differentiable Physics Part 2    • ETH Zürich DLSC: Introduction to Diff...  

Course tutorials: https://github.com/mroberto166/CAMLab...

▬ Course Learning Objectives ▬▬▬▬▬
The objective of this course is to introduce students to advanced applications of deep learning in scientific computing. The focus will be on the design and implementation of algorithms as well as on the underlying theory that guarantees reliability of the algorithms. We provide several examples of applications in science and engineering where deep learning based algorithms outperform state of the art methods.

By the end of the course you should be:
- Aware of advanced applications of deep learning in scientific computing
- Familiar with the design, implementation and theory of these algorithms
- Understand the pros/cons of using deep learning
- Understand key scientific machine learning concepts and themes