Request for Paper Implementation - Neural Operators

[Robertboy18]

I would like to request for an implementation of Fourier Neural Operators: https://arxiv.org/abs/2010.08895.

Neural operators are a class of deep learning architectures designed to learn maps between infinite-dimensional function spaces. Neural operators represent an extension of traditional artificial neural networks, marking a departure from the typical focus on learning mappings between finite-dimensional Euclidean spaces or finite sets. Neural operators directly learn operators between function spaces; they can receive input functions, and the output function can be evaluated at any discretization.

The primary application of neural operators is in learning surrogate maps for the solution operators of partial differential equations (PDEs), which are critical tools in modeling the natural environment. Standard PDE solvers can be time-consuming and computationally intensive, especially for complex systems. Neural operators have demonstrated improved performance in solving PDEs compared to existing machine learning methodologies while being significantly faster than numerical solvers. The operator learning paradigm allows learning maps between function spaces, and is different from parallel ideas of learning maps from finite-dimensional spaces to function spaces, and subsumes these settings when limited to fixed input resolution.

There is the neural operator library that we maintain (completely in Pytorch): https://github.com/neuraloperator/neuraloperator but I believe that it would be great to include a side by side example of a simple FNO architecture for the broader community to understand. Do let me know any way on how I can contribute to doing this.

Thank you