Discovering PDEs from Multiple Experiments

TL;DR

This paper presents a novel deep learning framework with a randomized group Lasso approach to discover PDEs that generalize across multiple experiments with inherent variability and noise.

Contribution

It introduces a grouped sparsity estimator that enables PDE discovery from multiple experiments, improving robustness and generalizability over traditional single-experiment methods.

Findings

More generalizable PDEs can be identified from noisy datasets.

Grouped sparsity promotion outperforms independent model discovery.

Framework handles inherent variability in experimental data.

Abstract

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters, initial and boundary conditions that cannot be simply averaged out. We introduce a randomised adaptive group Lasso sparsity estimator to promote grouped sparsity and implement it in a deep learning based PDE discovery framework. It allows to create a learning bias that implies the a priori assumption that all experiments can be explained by the same underlying PDE terms with potentially different coefficients. Our experimental results show more generalizable PDEs can be found from multiple highly noisy datasets, by this grouped sparsity promotion rather than simply performing independent model discoveries.