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

2026-04-28

AI Summary

This work addresses the inherent coupling between change-point detection and parameter estimation in nonlinear dynamical systems, which is commonly overlooked by traditional decoupled approaches. The authors propose a physics-informed neural network framework that jointly infers change points and segment-wise parameters through a two-stage strategy: first identifying candidate change-point regions via overlapping subinterval decomposition, then integrating these candidates into a unified optimization objective governed by a physics-based residual loss. This approach constitutes the first integration of change-point detection and parameter estimation within a physics-informed learning paradigm, leveraging localized residual anomalies to accurately pinpoint switching instants and solve the coupled inverse problem in an end-to-end manner. Experiments on benchmark systems—including Malthusian, Logistic, Van der Pol, Lotka–Volterra, and Lorenz models—demonstrate significant improvements over conventional decoupled methods in both change-point localization accuracy and parameter estimation fidelity.

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.

Problem

• change-point detection
• nonlinear dynamical systems
• regime switching
• parameter estimation
• inverse problems

Innovation

• physics-informed neural networks
• change-point detection
• regime switching
• residual-loss anomaly analysis
• joint parameter estimation