When Differentiable Programming Meets Spectral PDE Solver

We aim to combine data and physics for designing more accurate and faster PDE solvers. We reinterpret the data-driven machine learning approach of \cite{mishra2018machine} through a dynamical system perspective and draw a connection to neural ODE and implicit layer neural network architectures. These in turn inspire a class of sample-efficient spectral PDE solvers (with an encoder - processor - decoder structure) that can be trained end-to-end in a memory-efficient way. The crucial benefit of the methods is that they are resolution-invariant and guaranteed to be consistent.