Towards Multi-spatiotemporal-scale Generalized PDE Modeling
- URL: http://arxiv.org/abs/2209.15616v1
- Date: Fri, 30 Sep 2022 17:40:05 GMT
- Title: Towards Multi-spatiotemporal-scale Generalized PDE Modeling
- Authors: Jayesh K. Gupta, Johannes Brandstetter
- Abstract summary: We make a comparison between various FNO and U-Net like approaches on fluid mechanics problems in both vorticity-stream and velocity function form.
We show promising results on generalization to different PDE parameters and time-scales with a single surrogate model.
- Score: 4.924631198058705
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: Partial differential equations (PDEs) are central to describing complex
physical system simulations. Their expensive solution techniques have led to an
increased interest in deep neural network based surrogates. However, the
practical utility of training such surrogates is contingent on their ability to
model complex multi-scale spatio-temporal phenomena. Various neural network
architectures have been proposed to target such phenomena, most notably Fourier
Neural Operators (FNOs) which give a natural handle over local \& global
spatial information via parameterization of different Fourier modes, and U-Nets
which treat local and global information via downsampling and upsampling paths.
However, generalizing across different equation parameters or different
time-scales still remains a challenge. In this work, we make a comprehensive
comparison between various FNO and U-Net like approaches on fluid mechanics
problems in both vorticity-stream and velocity function form. For U-Nets, we
transfer recent architectural improvements from computer vision, most notably
from object segmentation and generative modeling. We further analyze the design
considerations for using FNO layers to improve performance of U-Net
architectures without major degradation of computational performance. Finally,
we show promising results on generalization to different PDE parameters and
time-scales with a single surrogate model.
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