Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data
This addresses the challenge of PDE discovery for researchers in computational science and engineering, but it appears incremental as it builds on existing weak form methods with adaptations for noise and data limitations.
The paper tackles the problem of discovering partial differential equations (PDEs) from noisy and limited data by introducing Weak-PDE-LEARN, an algorithm that uses a weak form-based adaptive loss function to train a neural network for solution approximation and PDE identification, demonstrating its efficacy on benchmark PDEs.
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.