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

Detecting regime shifts in chaotic time series is difficult 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. In Lorenz-63 with piecewise-constant parameters, Param-CPD improves F1, reduces localization error, and reduces false positives compared to baselines of observation-space. We further verify identifiability and calibration of the inferred posteriors on stationary trajectories, explaining why parameter space offers a cleaner detection signal. Robustness analyzes of 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.