Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurements

2026-06-14

AI Summary

This work proposes a weighted sparse regression framework for accurately identifying nonlinear dynamical systems from multi-fidelity observational data characterized by heterogeneous signal-to-noise ratios. The method introduces, for the first time within the Sparse Identification of Nonlinear Dynamics (SINDy) paradigm, a statistically principled weighting mechanism based on measurement uncertainties. By integrating Ensemble SINDy and Weak SINDy and employing generalized least squares, the approach adaptively weights observations of varying fidelity to effectively account for heteroscedastic noise. Theoretical analysis and numerical experiments demonstrate that properly weighted low-quality repeated measurements significantly enhance model recovery performance. Validation across multiple benchmark systems—including ordinary and partial differential equations—shows that the proposed method achieves prediction accuracy in complex systems such as the double pendulum that rivals or even surpasses that of conventional reconstruction techniques relying solely on high-fidelity data.

Abstract

Data from simulations and experiments are rarely noise-free and often exhibit heterogeneous levels of fidelity. Measurement uncertainty may vary across repeated observations, sensing devices, or even within a single experiment. This work addresses the problem of discovering nonlinear dynamical systems from such inhomogeneous data. We extend the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework to account for variable noise levels by combining Ensemble SINDy and Weak SINDy within a weighted regression formulation derived from generalized least squares. A statistical justification for the weighting strategy is also provided. The methodology is validated on several benchmark systems, including ordinary and partial differential equations. In addition, we show the benefit of multi-fidelity integration for forecasting the dynamics of a double pendulum system. The results confirm that the proposed approach mitigates the adverse effects of heteroscedastic noise and that repeated, low-cost, low-quality measurements can improve model recovery, in some cases matching or outperforming reconstructions obtained using only high-fidelity data.

Problem

• nonlinear dynamical systems
• heterogeneous data
• multi-fidelity
• noise
• system identification

Innovation

• Multi-Fidelity SINDy
• heteroscedastic noise
• weighted regression
• nonlinear dynamical systems
• Sparse Identification