PSI-SINDy: Post-Selection Inference for Sparse Identification of Nonlinear Dynamics
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.
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BibTeX
@misc{islam2026psisindy,
title = {{PSI-SINDy: Post-Selection Inference for Sparse Identification of Nonlinear Dynamics}},
author = {Ashraful Islam and Shuichi Nishino and Tomohiro Shiraishi and Ichiro Takeuchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11486},
eprint = {2610.11486},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11486},
}
RIS
TY - UNPB
TI - PSI-SINDy: Post-Selection Inference for Sparse Identification of Nonlinear Dynamics
AU - Ashraful Islam
AU - Shuichi Nishino
AU - Tomohiro Shiraishi
AU - Ichiro Takeuchi
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11486
UR - https://arxiv.org/abs/2610.11486
AB - 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.
ER -