Bayesian Sparse Identification of Time-varying Partial Differential Equations

doi:10.19596/j.cnki.1001-246x.8189

Abstract

Abstract: In data-driven modeling, Bayesian sparse identification method with Laplace priors was found and confirmed to recover sparse coefficients of governing partial differential equations(PDEs) by spatiotemporal data from measurement or simulation. Verification results of Bayesian sparse identification method for various canonical models (KdV equation, Burgers equation, Kuramoto-Sivashinsky equation, reaction-diffusion equations, nonlinear Schr dinger equation and Navier-Stokes equations) are compared with those of Rudy's PDE-FIND algorithm. Very well agreement between these two methods shows Bayesian sparse method has strong identification capability of PDE. However, it is also found that the Bayesian sparse method is much more sensitive to noise, which may identify more extra terms. In addition, relatively small error variances of Bayesian sparse solutions are obtained and exhibit clearly the successful identification of PDE.

Key words: Bayesian method, sparse identification, partial differential equation, Navier-Stokes equations

CLC Number:

HU Jun, LIU Quan, NI Guoxi. Bayesian Sparse Identification of Time-varying Partial Differential Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 38(1): 25-34.

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