Curation of resources for understanding Neural Operators. Here lies a list of papers and noteworthy resources for understanding Neural Operators. This list has been curated solely for self-use and serves as a "TODO" list of things to read and stuff I thought was useful that I can refer back to.
- PINNS: https://maziarraissi.github.io/PINNs/ (worth a read as it is one of the most influential papers in the field)
- Neural Ordinary Differential Equations: https://arxiv.org/abs/1806.07366 For this paper, I recommend watching the video first: https://www.youtube.com/watch?v=jltgNGt8Lpg&ab_channel=YannicKilcher
Here is a cool GitHub repo that keeps track of advancements in PINNS: https://github.com/idrl-lab/PINNpapers Operators:
- Fourier Neural Operators: https://arxiv.org/abs/2010.08895 This is the meat and potatoes of Neural Operators currently, and many works are extensions of this framework. I recommend watching https://www.youtube.com/watch?v=IaS72aHrJKE&ab_channel=YannicKilcher before you start reading the paper.
Here are some other alternative resources for these in case you want a different perspective: https://zongyi-li.github.io/neural-operator/ (contains links to other stuff that you may want to check out, like applications!)
- Clifford Neural Layers for PDE Modeling: https://arxiv.org/abs/2209.04934 This incorporates symmetries and the system's geometry into the mix. The paper can be quite heavy, so I recommend watching this talk: https://www.youtube.com/watch?v=VXziLgMIWf8&t=2597s&ab_channel=ValenceLabs Additionally, the series of blogs by the author was quite good for motivating Clifford NN: https://davidruhe.github.io/2023/01/05/hypercomplex-nns.html
What now? I recommend going through the tutorials provided by UVA to familiarise yourself with the code and its applications: https://uvadlc-notebooks.readthedocs.io/en/latest/. These are excellent resources in themselves if you want an introduction to a range of different topics in modern DL, and I always refer back to them!
Some other papers I want/am currently reading are: https://openreview.net/pdf?id=QJGj07PD9C Speedups in Fourier Neural Operators