Latent Neural PDE Solver for Time-Dependent Systems

Abstract

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). While many of the existing neural network surrogates operate on the high-dimensional discretized field, we propose to learn the dynamics of the system in the latent space with much coarser discretization. A non-linear autoencoder is trained first to project the full-order representation of the system onto the mesh-reduced space, then another temporal model is trained to predict the future state in this mesh-reduced space. This reduction process eases the training of the temporal model as it greatly reduces the computational cost induced by high-resolution discretization. We study the capability of the proposed framework on 2D/3D fluid flow and showcase that it has competitive performance compared to the model that operates on full-order space.