Sparse Identification of Nonlinear Dynamics with Conformal Prediction
This work addresses uncertainty quantification for SINDy models, which is essential for reliability in safety-critical applications, representing an incremental improvement by applying an existing framework to a specific method.
The paper tackles the problem of quantifying uncertainty in Sparse Identification of Nonlinear Dynamics (SINDy) models by integrating Conformal Prediction with Ensemble-SINDy, demonstrating that this approach reliably achieves desired coverage for time series forecasting, quantifies feature importance, and produces robust uncertainty intervals for model coefficients, even under non-Gaussian noise.
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.