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

Autor:	Stephany, Robert, Earls, Christopher
Rok vydání:	2023
Předmět:	Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.04699 Zobrazit plný text záznamu View this record from Arxiv