(Under construction)
To find our latest work on the subject, check out our paper on B-SINDy (Fung et al., 2025) and ODR-BINDy (Fung, 2025).
References
2025
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Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data
Lloyd Fung, Urban Fasel, and Matthew Juniper
Proc. R. Soc. A. Paper for the software package
B-SINDy , Feb 2025
We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the sparse identification of nonlinear dynamics (SINDy) method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as lynx–hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy.
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Overcoming error-in-variable problem in data-driven model discovery by orthogonal distance regression
Lloyd Fung
. Paper for the software package
ODR-BINDy , Feb 2025
