Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Xiangbo Deng, Cheng Chen, Peng Yang

TL;DR

This work tackles the challenge of detecting regime changes in chaotic, nonlinear time series where standard observation-space methods struggle due to intrinsic variability. It introduces Parameter-Space CPD (Param-CPD), a two-stage approach that uses simulation-based inference to amortize Bayesian parameter estimation over short windows and then applies a conventional CPD algorithm to the resulting parameter trajectory. Across Lorenz-63 experiments with piecewise-constant parameters, Param-CPD yields higher detection accuracy, tighter localization, and fewer false alarms than observation-space baselines, driven by well-calibrated posterior parameter estimates. The results suggest that operating in the physically meaningful parameter space yields more interpretable and robust changepoint detection, with potential applicability to real-world systems once simulators and scalability are addressed.

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.

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

TL;DR

This work tackles the challenge of detecting regime changes in chaotic, nonlinear time series where standard observation-space methods struggle due to intrinsic variability. It introduces Parameter-Space CPD (Param-CPD), a two-stage approach that uses simulation-based inference to amortize Bayesian parameter estimation over short windows and then applies a conventional CPD algorithm to the resulting parameter trajectory. Across Lorenz-63 experiments with piecewise-constant parameters, Param-CPD yields higher detection accuracy, tighter localization, and fewer false alarms than observation-space baselines, driven by well-calibrated posterior parameter estimates. The results suggest that operating in the physically meaningful parameter space yields more interpretable and robust changepoint detection, with potential applicability to real-world systems once simulators and scalability are addressed.

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.
Paper Structure (26 sections, 2 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 26 sections, 2 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Changepoint Detection in Time Series
  4. From Observations to Parameters: The Role of Representation Learning
  5. System Identification and Parameter Estimation
  6. Simulation-Based Inference for Parameter Estimation
  7. Methodology
  8. Overview of the Parameter-Space CPD Framework
  9. Problem Formulation
  10. Stage 1: Offline Training of the Neural Posterior Estimator
  11. Stage 2: Parameter Estimation and CPD
  12. Experiments
  13. Research Questions
  14. Datasets
  15. Changepoint Sequences
  16. ...and 11 more sections

Figures (4)

  • Figure 1: Case study on Lorenz--63 with $\sigma$-changepoints ($w{=}100$, $s{=}1$, $\delta{=}10$, $\eta{=}1\%$). (a) Standardized and smoothed $x(t)$ with bottom Ground-truth tick rail. (b) Posterior mean $\hat{\sigma}(t)$; gray bands mark the low/high parameter ranges. (c) Changepoints: Ground truth (black), Param-CPD (green), Obs-CPD (orange). The three panels share the same time-step axis; only the bottom panel shows ticks.
  • Figure 2: Quantitative summary across changepoint types. (a) F1@$\,\delta$ for $\sigma/\rho/\beta$. (b) MAE (steps; lower is better). (c) FP per 1000 steps (lower is better). Param-CPD (green) vs Obs-CPD (orange).
  • Figure 3: Posterior parameter accuracy across $\sigma/\rho/\beta$. Each panel scatters posterior estimates $\hat{\theta}$ versus ground truth $\theta$, with the diagonal $y{=}x$ and an OLS calibration line.
  • Figure 4: F1--$\delta$ curves across changepoint types. Param-CPD (green solid) vs Obs-CPD (orange dashed) over $\sigma/\rho/\beta$; the gray dotted vertical line marks the reference $\delta$.