PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning

TL;DR

PDE-READ introduces a deep learning framework with neural networks and sparse regression to discover human-readable PDEs from sparse, noisy data, demonstrating robustness and applicability to real-world systems.

Contribution

The paper presents a novel approach combining Rational Neural Networks and sparse regression for PDE discovery, improving robustness to data sparsity and noise.

Findings

Successfully identified PDEs in six benchmark examples.

Robust to data sparsity and noise.

Open-source implementation available.

Abstract

PDE discovery shows promise for uncovering predictive models of complex physical systems but has difficulty when measurements are sparse and noisy. We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a principled sparse regression algorithm to identify the hidden dynamics that govern a system's response. The first network learns the system response function, while the second learns a hidden PDE describing the system's evolution. We then use a parameter-free sparse regression algorithm to extract a human-readable form of the hidden PDE from the second network. We implement our approach in an open-source library called PDE-READ. Our approach successfully identifies the governing PDE in six benchmark examples. We demonstrate that our approach is robust to both sparsity and noise and it, therefore, holds promise for application to real-world observational data.