Authors: Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, Anima Anandkumar

Published on: May 03, 2024

Impact Score: 7.8

Arxiv code: Arxiv:2207.05209

Summary

• What is new: A new framework, geo-FNO, that can solve PDEs on arbitrary geometries, improving both the speed and accuracy of solutions compared to existing methods.
• Why this is important: Existing deep learning models like the Fourier neural operator (FNO) are limited to rectangular domains with uniform grids, restricting their application to complex geometries.
• What the research proposes: Geo-FNO expands the application of FNO to irregular geometries by deforming the input domain into a latent space where the FFT can be applied, making it versatile and efficient.
• Results: Geo-FNO achieved a speed 100,000 times faster than standard numerical solvers and was twice as accurate compared to existing ML-based PDE solvers like the standard FNO.

Technical Details

Technological frameworks used: Geo-FNO

Models used: Fourier Neural Operator (FNO) with Fast Fourier Transform (FFT)

Data used: Point clouds, meshes, and design parameters

Potential Impact

Engineering design and simulation software, aerospace, civil engineering, and any industry relying on PDE modeling for fluid dynamics or material science.

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