CP-PINNs: Data-Driven Changepoints Detection in PDEs Using Online Optimized Physics-Informed Neural Networks
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Meta-Learningparameter estimationSimilar Papers 제목 키워드 기반
An efficient hp-Variational PINNs framework for incompressible Navier-Stokes equations
Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs)…
Curriculum Learning-Driven PIELMs for Fluid Flow Simulations
This paper presents two novel, physics-informed extreme learning machine (PIELM)-based algorithms for solving steady and unsteady nonlinear partial differential equations (PDEs) related to fluid flow. Although single-hid…
PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers
With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently eme…
SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decomposition
Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in tradition…
Transfer LearningRevisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method
Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remai…