Structural Change Detection in Dynamic Systems

2026-06-25

AI Summary

Existing methods struggle to effectively detect structural breaks in dynamical systems driven by nonlinear, nonstationary trajectories arising from external interventions or environmental shifts. This work proposes a unified framework that, for the first time, jointly models residual discrepancies and normalized parameter drifts to construct a test statistic. By integrating a multi-scale seeded narrowest-over-threshold algorithm, order-preserving segmentation, and symmetric contrastive calibration, the method achieves precise localization of structural changes in ordinary differential equation–driven systems. It simultaneously accounts for model fit and evidence of parameter variation, demonstrating robustness under both stable and divergent trajectories while attaining near-minimax localization accuracy and effective false discovery rate (FDR) control. Experiments show significant improvements over state-of-the-art approaches in detection accuracy and FDR management, with successful applications to modeling COVID-19 transmission dynamics and global temperature trends.

Abstract

Structural changes often arise in real-world dynamic systems due to external interventions or environmental shifts, such as policy changes in epidemiology or climate forcing in environmental science. In this paper, we propose a unified framework for detecting and localizing structural changes in dynamic systems governed by ordinary differential equations. Unlike existing methods that assume mean or linear trend changes, our approach accommodates complex, nonlinear dynamics with both stable and diverging trajectories. We develop a new test statistic that combines residual-based discrepancy and normalized parameter contrast, capturing evidence for structural changes from both model fit and parameter shifts. Candidate structural changes are efficiently screened using a multiscale seeded-narrowest-over-threshold algorithm with a data-driven thresholding strategy. To refine selections and control false discoveries, we introduce a false discovery rate control procedure that leverages order-preserved sample splitting and symmetric contrast calibration. Theoretical guarantees are established, including detection consistency, near-minimax localization accuracy, and valid FDR control under weak dependence. Extensive simulations demonstrate superior performance over existing methods in both accuracy and FDR control. Applications to real-world data sets, including COVID-19 dynamics and global temperature trends, highlight the practical relevance and broad applicability of our method.

Problem

• structural change detection
• dynamic systems
• nonlinear dynamics
• ordinary differential equations
• change point localization

Innovation

• structural change detection
• nonlinear dynamics
• false discovery rate control
• multiscale change-point screening
• parameter contrast