Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session R29: Modeling Methods I: Closure Models, Automated Discovery of Equations, and Prediction
1:50 PM–3:34 PM,
Monday, November 20, 2023
Room: 152B
Chair: Sarah Beetham, Oakland University
Abstract: R29.00005 : Bayesian Identification of Nonlinear Dynamics (BINDy)*
2:42 PM–2:55 PM
Presenter:
Lloyd Fung
(Univ of Cambridge)
Authors:
Lloyd Fung
(Univ of Cambridge)
Urban Fasel
(Imperial College London)
Matthew P Juniper
(Univ of Cambridge)
We propose a Bayesian extension to SINDy for learning sparse equations from data. Our method shows more robust capability in learning the correct model in the low-data limit, as it sparsifies the model based on both the value and the distribution of the parameters during regression, and uses the marginal likelihood (evidence) to rank and select the candidate models. The proposed method uses Laplace's method to approximate the Bayesian likelihood and evidence, avoiding the need for computationally expensive Markov chain Monte Carlo (MCMC) sampling. This results in a significant speedup in computation compared to other Bayesian SINDy methods, while still achieving comparable or better performance than existing methods such as Ensemble-SINDy.
We demonstrate the effectiveness of the proposed method on a variety of problems, including learning the Lotka-Volterra equations from 21 experimental data points of the Hudson Bay Lynx-Hare population dataset, and the Lorenz system using tens of noisy data points. We also apply the method to a real-life dataset in fluids, such as the measurements of the quasi-2D Kolmogorov-like flow, showing how it can learn both the high-order equations and low-order dynamics with just a tiny subset of the data.
*LF is funded by the Research Fellowship from Peterhouse, University of Cambridge.
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