PSI-SINDy: Post-Selection Inference for Sparse Identification of Nonlinear Dynamics

2026-10-08

AI Summary

This study addresses the failure of statistical inference for dynamical terms in Sparse Identification of Nonlinear Dynamics (SINDy) models caused by selection bias, measurement error, and shared noise. To overcome these challenges, we propose PSI-SINDy, the first post-selection inference framework tailored for SINDy. By integrating post-selection inference theory with data thinning techniques, the method decomposes trajectories into four independent views, effectively mitigating interference from shared noise between the design matrix and the response variable. This enables unbiased hypothesis testing and confidence interval estimation. Theoretical analysis establishes the validity of the proposed approach, while both simulation studies and real-world experiments demonstrate its superior inferential accuracy and robustness.

Abstract

Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for discovering governing dynamics from time-series data by identifying a sparse subset of candidate dynamical terms from a prespecified library. In this work, we develop a statistical inference framework for quantifying the reliability of dynamical terms selected by SINDy through hypothesis tests and confidence intervals. A key difficulty is that using the same noisy trajectory for both selecting dynamical terms and assessing their statistical significance can introduce selection bias. Post-selection inference provides a principled framework for addressing such bias, and we propose PSI-SINDy, a post-selection inference method tailored to SINDy. Direct application of existing post-selection inference techniques is challenging because SINDy involves measurement error in the candidate terms and shared noise between the response and design. To address these challenges, PSI-SINDy uses data thinning to decompose a single observed trajectory into four mutually independent views with distinct roles in selection and inference. This construction enables inference for selected dynamical terms while accounting not only for selection bias but also for measurement-error and shared noise effects. We establish the theoretical validity of PSI-SINDy under stated conditions and evaluate its performance through numerical experiments on simulated and experimental dynamical-system data.

Problem

• Sparse Identification of Nonlinear Dynamics
• Post-Selection Inference
• Selection Bias
• Measurement Error
• Statistical Reliability

Innovation

• Post-Selection Inference
• SINDy
• Data Thinning
• Sparse Identification
• Measurement Error