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ETH Zürich Deep Learning in Scientific Computing 2023
Lecture 11: Fourier Neural Operators and Convolutional Neural Operators

Lecturers: Ben Moseley and Siddhartha Mishra

▬ Lecture Content ▬▬▬▬▬▬▬▬▬
0:00 - Recap: previous lecture
4:47 - Theoretical properties of Fourier neural operators (FNOs)
9:59 - DeepONets vs FNOs
19:35 - Issues with FNOs
26:20 - Aliasing in FNOs
40:57 - Convolutional neural operators (CNOs)
50:15 - CNO architectures in practice
57:09 - Performance of CNOs
1:13:41 - Open issues in operator learning

▬ 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