Residual-loss Anomaly Analysis of Physics-Informed Neural Networks: An Inverse Method for Change-point Detection in Nonlinear Dynamical Systems with Regime Switching

• URL: http://arxiv.org/abs/2604.25655v1
• Date: Tue, 28 Apr 2026 13:50:50 GMT
• Title: Residual-loss Anomaly Analysis of Physics-Informed Neural Networks: An Inverse Method for Change-point Detection in Nonlinear Dynamical Systems with Regime Switching
• Abstract summary: We propose a unified framework for residual-loss anomaly analysis of physics-informed neural networks.<n>This approach jointly infers piecewise parameters and transition points under a single set of constraints.<n>We show that the proposed method outperforms traditional decoupled approaches in both change-point localization and parameter estimation accuracy.
• Score: 10.645192584041162
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate tasks, ignoring the inherent coupling between them. To address this, we propose residual-loss anomaly analysis of physics-informed neural networks, a unified framework that leverages dynamical consistency within the physics-informed learning paradigm. This approach jointly infers piecewise parameters and transition points under a single set of constraints. The method follows a two-stage strategy: First, local physical residuals are analyzed through overlapping subinterval decomposition. When a subinterval spans a true transition point, the residual exhibits a distinct structural elevation in noise-free conditions, which has a non-zero lower bound, enabling effective localization of potential transition intervals. Second, within our framework, change-point locations and piecewise parameters are integrated into a unified physical loss function for joint optimization, enabling simultaneous identification. Experiments on benchmark nonlinear dynamical systems, including Malthusian and logistic growth models, Van der Pol oscillator, Lotka-Volterra model and Lorenz system, demonstrate that the proposed method outperforms traditional decoupled approaches in both change-point localization and parameter estimation accuracy. This study provides an efficient, unified solution for structurally coupled inverse problems in nonlinear dynamical systems with regime switching.

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