Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurements
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 25 of its 61 references that are in the map. First posted on arXiv 14 Jun 2026.
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25 of 61 references.
References · 25
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13 more
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- 2023Residual Multi-Fidelity Neural Network Computingcited by 5
- 2024Sparse discovery of differential equations based on multi-fidelity Gaussian processcited by 5
- 2025Multi-Level Monte Carlo Training of Neural Operatorscited by 4
- 2024Multifidelity linear regression for scientific machine learning from scarce datacited by 3
- 2025Noise-robust multi-fidelity surrogate modelling for parametric partial differential equationscited by 2
- 2025Progressive multi-fidelity learning with neural networks for physical system predictionscited by 2
- 2025Assessing the performance of correlation-based multi-fidelity neural emulatorscited by 2
- 2024Confidence Intervals for the Savitzky-Golay Filter with an Application to the Keeling Data for Atmospheric CO2cited by 1
- 2025Weighted Birkhoff Averages Accelerate Data-Driven Methodscited by 1
- 2025Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networkscited by 1
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