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ETH Zürich Deep Learning in Scientific Computing 2023
Lecture 6: Physics-Informed Neural Networks - Limitations and Extensions
Course Website (links to slides and tutorials): https://camlab.ethz.ch/teaching/deep-learning-in-scientific-computing-2023.html
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 https://www.youtube.com/watch?v=y6wHpRzhhkA&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=1
Lecture 2: Introduction to Deep Learning Part 1 https://www.youtube.com/watch?v=q8bAXSBRz3k&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=2
Lecture 3: Introduction to Deep Learning Part 2 https://www.youtube.com/watch?v=GWjnFVIGwIg&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=3
Lecture 4: Physics-Informed Neural Networks - Introduction https://www.youtube.com/watch?v=Oh1nhCNlqjg&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=4
Lecture 5: Physics-Informed Neural Networks - Applications https://www.youtube.com/watch?v=IDIv92Z6Qvc&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=5
Lecture 6: Physics-Informed Neural Networks - Limitations and Extensions https://www.youtube.com/watch?v=FAfVbrufiZM&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=6
Lecture 7: Introduction to Operator Learning Part 1 https://www.youtube.com/watch?v=MUYpmqXtJWs&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=7
Lecture 8: Introduction to Operator Learning Part 2 https://www.youtube.com/watch?v=kGACWUjHHMY&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=8
Lecture 9: Deep Operator Networks https://www.youtube.com/watch?v=f0nh-4EaJFI&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=9
Lecture 10: Neural Operators https://www.youtube.com/watch?v=QaCfIZl9XEo&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=10
Lecture 11: Fourier Neural Operators and Convolutional Neural Operators https://www.youtube.com/watch?v=K-ZAKqzptTE&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=11
Lecture 12: Introduction to Differentiable Physics Part 1 https://www.youtube.com/watch?v=1Edfts3UzaY&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=12
Lecture 13: Introduction to Differentiable Physics Part 2 https://www.youtube.com/watch?v=iQ96Bil0rjE&list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&index=13
▬ 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