Rapid Bayesian identification of sparse nonlinear dynamics from scarce
and noisy data
- URL: http://arxiv.org/abs/2402.15357v1
- Date: Fri, 23 Feb 2024 14:41:35 GMT
- Title: Rapid Bayesian identification of sparse nonlinear dynamics from scarce
and noisy data
- Authors: Lloyd Fung, Urban Fasel, Matthew P. Juniper
- Abstract summary: We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation.
The resulting method, Bayesian-SINDy, quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data.
- Score: 2.5870115809699787
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose a fast probabilistic framework for identifying differential
equations governing the dynamics of observed data. We recast the 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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