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

A team led by Yuhe Bai and Zhikun Zhang from multiple institutions has introduced a novel framework called residual-loss anomaly analysis of physics-informed neural networks (PINNs) for detecting change-points in nonlinear dynamical systems with regime switching. Traditional approaches treat change-point detection and parameter estimation as separate tasks, ignoring their inherent coupling. The new method unifies them under a physics-informed learning paradigm, leveraging dynamical consistency to jointly infer piecewise parameters and transition points from 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 with a non-zero lower bound in noise-free conditions, enabling effective localization of potential transition intervals. Second, change-point locations and piecewise parameters are integrated into a unified physical loss function for joint optimization, enabling simultaneous identification. Experiments on benchmark systems including Malthusian and logistic growth models, the 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 provides an efficient, unified solution for structurally coupled inverse problems in nonlinear dynamical systems with regime switching.