CP-PINNs: Changepoints Detection in PDEs using Physics Informed Neural Networks with Total-Variation Penalty

The paper shows that Physics-Informed Neural Networks (PINNs) can fail to estimate the correct Partial Differential Equations (PDEs) dynamics in cases of unknown changepoints in the parameters. To address this, we propose a new CP-PINNs model which integrates PINNs with Total-Variation penalty for accurate changepoints detection and PDEs discovery. In order to optimally combine the tasks of model fitting, PDEs discovery, and changepoints detection, we develop a new meta-learning algorithm that exploits batch learning to dynamically refines the optimization objective when moving over the consecutive batches of the data. Empirically, in case of changepoints in the dynamics, our approach demonstrates accurate parameter estimation and model alignment, and in case of no changepoints in the data, it converges numerically to the solution from the original PINNs model.