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

arXiv:2402.17853v1 Announce Type: new
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 …

abstract arxiv cs.ai cs.lg differential dynamics fields framework learn math.ap modelling network networks neural network neural networks numerical simulation solver systems type