Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations
This work addresses computational bottlenecks in PDE simulation for fields like fluid dynamics, though it is incremental as it builds on existing neural network surrogates.
The paper tackles the problem of accelerating numerical simulation of partial differential equations (PDEs) by proposing a reduced-order modeling framework that learns dynamics in a latent space with coarser discretizations, resulting in competitive accuracy and efficiency compared to full-order neural PDE solvers.
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.