Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From
  Noisy, Limited Data
Robert Stephany Christopher Earls
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.