Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations

TL;DR

The paper introduces Latent Neural PDE Solver, a reduced-order modeling framework that learns system dynamics in a lower-dimensional latent space to accelerate PDE simulations while maintaining accuracy.

Contribution

It proposes a novel framework combining autoencoders and temporal models for efficient PDE simulation in a reduced latent space, improving computational efficiency.

Findings

Competitive accuracy with full-order neural PDE solvers

Significant reduction in computational cost

Effective across various flow systems

Abstract

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional discretized fields, we propose to learn the dynamics of the system in the latent space with much coarser discretizations. In our proposed framework - Latent Neural PDE Solver (LNS), a non-linear autoencoder is first trained to project the full-order representation of the system onto the mesh-reduced space, then a temporal model is trained to predict the future state in this mesh-reduced space. This reduction process simplifies the training of the temporal model by greatly reducing the computational cost accompanying a fine discretization. We study the capability of the proposed framework and several other popular neural PDE solvers on various types of systems including single-phase and multi-phase flows along with varying system parameters. We showcase that it has competitive accuracy and efficiency compared to the neural PDE solver that operates on full-order space.