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Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
May 3, 2024, 4:54 a.m. | Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, Anima Anandkumar
cs.LG updates on arXiv.org arxiv.org
Abstract: Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs, such as fluid flows. However, the FNO uses the Fast Fourier transform (FFT), which is limited to rectangular domains with uniform grids. In this work, we propose a new framework, viz., geo-FNO, to solve PDEs on arbitrary geometries. Geo-FNO …
abstract accuracy arxiv cs.lg cs.na deep learning differential faster fourier general good however math.na numerical them type
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