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

• URL: http://arxiv.org/abs/2402.17853v1
• Date: Tue, 27 Feb 2024 19:36:27 GMT
• Title: Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations
• Authors: Zijie Li, Saurabh Patil, Francis Ogoke, Dule Shu, Wilson Zhen, Michael Schneier, John R. Buchanan, Jr., Amir Barati Farimani
• Abstract summary: We propose to learn the dynamics of the system in the latent space with much coarser discretizations. A non-linear autoencoder is first trained to project the full-order representation of the system onto the mesh-reduced space. We showcase that it has competitive accuracy and efficiency compared to the neural PDE solver that operates on full-order space.
• Score: 6.173339150997772
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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