Sparse Identification of Nonlinear Dynamics with Conformal Prediction

TL;DR

This paper integrates conformal prediction with Ensemble-SINDy to provide reliable uncertainty quantification in nonlinear dynamical system modeling, enhancing robustness and coverage guarantees in various applications.

Contribution

It introduces a novel framework combining conformal prediction with E-SINDy for uncertainty quantification in nonlinear dynamics, applicable to time series, model selection, and coefficient estimation.

Findings

Conformal prediction achieves target coverage in time series forecasting.

The method effectively quantifies feature importance in models.

Uncertainty intervals for coefficients are more robust under non-Gaussian noise.

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.