When Differentiable Programming Meets Spectral PDE Solver

Abstract

We aim to combine data and physics for designing more accurate and faster PDE solvers. We reinterpret the data-driven machine learning approach of \cite{mishra2018machine} through a dynamical system perspective and draw a connection to neural ODE and implicit layer neural network architectures. These in turn inspire a class of sample-efficient spectral PDE solvers (with an encoder - processor - decoder structure) that can be trained end-to-end in a memory-efficient way. The crucial benefit of the methods is that they are resolution-invariant and guaranteed to be consistent.

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Cite

Text

Jiang. "When Differentiable Programming Meets Spectral PDE Solver." NeurIPS 2024 Workshops: D3S3, 2024.

Markdown

[Jiang. "When Differentiable Programming Meets Spectral PDE Solver." NeurIPS 2024 Workshops: D3S3, 2024.](https://mlanthology.org/neuripsw/2024/jiang2024neuripsw-differentiable/)

BibTeX

@inproceedings{jiang2024neuripsw-differentiable,
  title     = {{When Differentiable Programming Meets Spectral PDE Solver}},
  author    = {Jiang, Qijia},
  booktitle = {NeurIPS 2024 Workshops: D3S3},
  year      = {2024},
  url       = {https://mlanthology.org/neuripsw/2024/jiang2024neuripsw-differentiable/}
}