PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning
This addresses the challenge of PDE discovery for complex physical systems using observational data, representing an incremental improvement in method robustness.
The researchers tackled the problem of discovering partial differential equations (PDEs) from sparse and noisy measurements by introducing PDE-READ, which uses two Rational Neural Networks and sparse regression to identify hidden dynamics. Their approach successfully identified governing PDEs in six benchmark examples and demonstrated robustness to sparsity and noise.
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.