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

TL;DR

This paper introduces Param--CPD, a novel two-stage framework that improves changepoint detection in nonlinear dynamical systems by inferring parameters in a physically interpretable space, outperforming observation-space methods.

Contribution

The paper proposes a new parameter-space changepoint detection method that combines simulation-based Bayesian inference with standard CPD algorithms, enhancing accuracy and interpretability.

Findings

Param--CPD outperforms observation-space baselines in Lorenz--63.

It reduces localization error and false positives.

Parameter space offers a cleaner detection signal.

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.