Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data

Robert Stephany, Christopher Earls
9/9/2023
cs.LG

Official code: punkduckable/Weak_PDE_LEARN (5 stars, last commit 2024-02-12).

Abstract

We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms to train a neural network, $U$, to approximate the PDE solution while simultaneously identifying the governing PDE. This approach yields an algorithm that is robust to noise and can discover a range of PDEs directly from noisy, limited measurements of their solutions. We demonstrate the efficacy of Weak-PDE-LEARN by learning several benchmark PDEs.

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Code Implementations(1)

punkduckable/Weak_PDE_LEARNOfficial
50MATLAB, PythonApr 11, 20222 years ago

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Cite this paper

@article{stephany2023weakpdelearn,
  title  = {Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data},
  author = {Robert Stephany and Christopher Earls},
  year   = {2023},
  eprint = {2309.04699},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2309.04699v1}
}

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