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.

翻译：本文表明，在参数存在未知变点的情况下，物理信息神经网络（PINNs）可能无法正确估计偏微分方程（PDEs）的动态行为。为解决这一问题，我们提出了一种新的CP-PINNs模型，该模型将PINNs与全变分惩罚相结合，以实现精确的变点检测和PDEs发现。为了最优地结合模型拟合、PDEs发现和变点检测等任务，我们开发了一种新的元学习算法，该算法利用批量学习在数据连续批次的推进过程中动态优化优化目标。实验表明，在动态存在变点的情况下，我们的方法实现了准确的参数估计和模型对齐；而在数据中无变点时，该方法数值上收敛于原始PINNs模型的解。