SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:428

Article

Zhang, Sheng¹  Lin, Guang^1,2 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA

关键词: Machine learning;    Data-driven discovery;    Bayesian inference;    Subsampling;    High noise;    Outlier;   

DOI  :  10.1016/j.jcp.2020.109962

来源: Elsevier

【 摘 要 】

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has two parameters: subsampling size and the number of subsamples. When the subsampling size increases with fixed total sample size, the accuracy of our algorithm goes up and then down. When the number of subsamples increases, the accuracy of our algorithm keeps going up. We demonstrate how to use our algorithm step by step and compare our algorithm with threshold sparse Bayesian regression (TSBR) for the discovery of differential equations. We show that our algorithm produces better results. We also discuss the merits of discovering differential equations from data and demonstrate how to discover models with random initial and boundary condition as well as models with bifurcations. The numerical examples are: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary condition, and (4) fish-harvesting problem with bifurcations. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free