From Observations to Parameters: Detecting Changepoint in Nonlinear Dynamics with Simulation-based Inference

2025-10-20

AI Summary

In chaotic time series, observational signals are highly coupled with underlying dynamical variability, rendering conventional observation-space change-point detection ineffective for identifying mechanistic transitions. To address this, we propose an interpretable parameter-space paradigm: using simulation-based Bayesian inference with a neural posterior estimator to map observed sequences onto dynamic parameter trajectories, followed by standard change-point detection on these trajectories. Our method integrates neural posterior estimation, simulation-based inference, and off-the-shelf change-point algorithms, and is validated on the Lorenz-63 system. Compared to observation-space baselines, it achieves significant improvements in F1 score, localization accuracy, and false positive rate. We further demonstrate posterior identifiability and calibration, robustness to noise and hyperparameter variation, and a unique balance of high statistical accuracy and physical interpretability.

Technology Category

Intelligent Robots: State EstimationMachine Learning: Calibration & Uncertainty QuantificationSearch and Optimization: Sampling/Simulation-based Search

Application Category

User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Models for Web evolution

Abstract

Detecting regime shifts in chaotic time series is hard because observation-space signals are entangled with intrinsic variability. We propose Parameter--Space Changepoint Detection (Param--CPD), a two--stage framework that first amortizes Bayesian inference of governing parameters with a neural posterior estimator trained by simulation-based inference, and then applies a standard CPD algorithm to the resulting parameter trajectory. On Lorenz--63 with piecewise-constant parameters, Param--CPD improves F1, reduces localization error, and lowers false positives compared to observation--space baselines. We further verify identifiability and calibration of the inferred posteriors on stationary trajectories, explaining why parameter space offers a cleaner detection signal. Robustness analyses over tolerance, window length, and noise indicate consistent gains. Our results show that operating in a physically interpretable parameter space enables accurate and interpretable changepoint detection in nonlinear dynamical systems.

Problem

• Detecting regime shifts in chaotic nonlinear dynamical systems
• Disentangling observation signals from intrinsic chaotic variability
• Enabling interpretable changepoint detection through parameter space analysis

Innovation

• Amortizes Bayesian inference using neural posterior estimator
• Applies changepoint detection to parameter trajectories
• Leverages simulation-based inference for nonlinear dynamics