Neural Operators for Solving PDEs and Inverse Design

Deep learning surrogate models have shown promise in modeling complex physical phenomena such as photonics, fluid flows, molecular dynamics and material properties. However, standard neural networks assume finite-dimensional inputs and outputs, and hence, cannot withstand a change in resolution or discretization between training and testing. We introduce Fourier neural operators that can learn operators, which are mappings between infinite dimensional spaces. They are discretization-invariant and can generalize beyond the discretization or resolution of training data. They can efficiently solve partial differential equations (PDEs) on general geometries. We consider a variety of PDEs for both forward modeling and inverse design problems, as well as show practical gains in the lithography domain.