  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.
