Summary of Physics-embedded Fourier Neural Network For Partial Differential Equations, by Qingsong Xu et al.
Physics-embedded Fourier Neural Network for Partial Differential Equations
by Qingsong Xu, Nils Thuerey, Yilei Shi, Jonathan Bamber, Chaojun Ouyang, Xiao Xiang Zhu
First submitted to arxiv on: 15 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A novel frequency domain-based approach called Physics-embedded Fourier Neural Networks (PeFNN) is proposed to solve complex spatiotemporal dynamical systems governed by partial differential equations (PDEs). PeFNN addresses the shortcomings of existing methods, which neglect physical laws and lack interpretability. The model incorporates momentum conservation and yields interpretable nonlinear expressions through the use of multi-scale momentum-conserving Fourier (MC-Fourier) layers and element-wise product operation. This plug-and-play module adheres to the laws of momentum conservation, making it a valuable tool for solving widely employed spatiotemporal PDEs. PeFNN establishes a new state-of-the-art in solving these types of problems and generalizes well across input resolutions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new way to solve complex systems is developed using Fourier neural operators. This approach is different from others because it follows physical laws and can be understood. The model is called Physics-embedded Fourier Neural Networks (PeFNN) and uses something called MC-Fourier layers. These layers make sure the model works with momentum conservation, which is important in some fields like flood simulations. |
Keywords
* Artificial intelligence * Spatiotemporal
