# CP-PINNs: Data-Driven Changepoints Detection in PDEs Using Online Optimized Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2208.08626 · HTML: https://mlsanity.com/paper/2208.08626/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 73 references that are in the map.
- First posted on arXiv 18 Aug 2022.

## Builds on (most cited first, 17 of 17)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization](https://mlsanity.com/paper/2112.14368/) (2021)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Adaptive piecewise polynomial estimation via trend filtering](https://mlsanity.com/paper/1304.2986/) (2013)
- [Nonlinear Approximation and (Deep) ReLU Networks](https://mlsanity.com/paper/1905.02199/) (2019)
- [Random Forests for Change Point Detection](https://mlsanity.com/paper/2205.04997/) (2022)
- [Function approximation by deep networks](https://mlsanity.com/paper/1905.12882/) (2019)
- [Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models](https://mlsanity.com/paper/1711.07357/) (2017)
- [Machine Learning and Cosmology](https://mlsanity.com/paper/2203.08056/) (2022)
- [Massively parallel solvers for elliptic PDEs in Numerical Weather- and Climate Prediction](https://mlsanity.com/paper/1307.2036/) (2013)

## Built on by (most cited first, 3 of 3)

- [Journey into Automation: Image-Derived Pavement Texture Extraction and Evaluation](https://mlsanity.com/paper/2501.02414/) (2025)
- [ChromouVQA: Benchmarking Vision-Language Models under Chromatic Camouflaged Images](https://mlsanity.com/paper/2512.05137/) (2025)
- [Inverse Problems for Partial Differential Equations with Jump Discontinuities in Coefficients via Two-Stage Physics-Informed Deep Learning and Statistical Mixture Models](https://mlsanity.com/paper/2510.14656/) (2025)

## Abstract (arXiv)

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal approximators capable of estimating the solution of any physical law described by a system of PDEs, which serves as a regularization during neural network training, restricting the space of admissible solutions and enhancing function approximation accuracy. We demonstrate that when the system exhibits sudden changes in the PDE dynamics, this regularization is either insufficient to accurately estimate the true dynamics, or it may result in model miscalibration and failure. Consequently, we propose a PINNs extension using a Total-Variation penalty, which allows to accommodate multiple changepoints in the PDE dynamics and significantly improves function approximation. These changepoints can occur at random locations over time and are estimated concurrently with the solutions. Additionally, we introduce an online learning method for re-weighting loss function terms dynamically. Through empirical analysis using examples of various equations with parameter changes, we showcase the advantages of our proposed model. In the absence of changepoints, the model reverts to the original PINNs model. However, when changepoints are present, our approach yields superior parameter estimation, improved model fitting, and reduced training error compared to the original PINNs model.