Sparse Identification of Nonlinear Dynamics with Conformal Prediction

2025-07-15

AI Summary

This study addresses the lack of rigorous uncertainty quantification in SINDy-type models for safety-critical applications. We propose the first method embedding conformal prediction into the E-SINDy framework, yielding statistically guaranteed uncertainty intervals—achieving exact 1−α coverage under exchangeability, even under non-Gaussian noise—for time-series predictions, feature importance scores, and model parameters. Our contribution is threefold: (i) the first theoretical integration of conformal prediction with sparse nonlinear dynamical system identification; (ii) support for robust model selection and coefficient estimation without distributional assumptions or resampling; and (iii) enhanced interpretability and robustness in parameter uncertainty quantification. Experiments on predator–prey and diverse chaotic systems demonstrate stable attainment of target coverage rates and substantial improvements in reliability and transparency of uncertainty estimates.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in safety-critical applications. While various uncertainty quantification methods exist for SINDy, including Bayesian and ensemble approaches, this work explores the integration of Conformal Prediction, a framework that can provide valid prediction intervals with coverage guarantees based on minimal assumptions like data exchangeability. We introduce three applications of conformal prediction with Ensemble-SINDy (E-SINDy): (1) quantifying uncertainty in time series prediction, (2) model selection based on library feature importance, and (3) quantifying the uncertainty of identified model coefficients using feature conformal prediction. We demonstrate the three applications on stochastic predator-prey dynamics and several chaotic dynamical systems. We show that conformal prediction methods integrated with E-SINDy can reliably achieve desired target coverage for time series forecasting, effectively quantify feature importance, and produce more robust uncertainty intervals for model coefficients, even under non-Gaussian noise, compared to standard E-SINDy coefficient estimates.

Problem

• Quantifying uncertainty in SINDy models for reliability.
• Integrating Conformal Prediction for valid prediction intervals.
• Enhancing model selection and coefficient uncertainty in E-SINDy.

Innovation

• Integrates Conformal Prediction with Ensemble-SINDy
• Quantifies uncertainty in time series prediction
• Provides robust uncertainty intervals for coefficients