Bayesian data-driven discovery of partial differential equations with variable coefficients

arXiv:2102.01432v2 Announce Type: replace-cross
Abstract: The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered equation to noise and the complexities of model selection. In this work, we propose an advanced Bayesian sparse learning algorithm for PDE discovery with variable coefficients, predominantly when the coefficients are spatially or temporally dependent. Specifically, we apply threshold Bayesian group Lasso regression …

abstract arxiv bayesian complexities cs.lg data data-driven differential discovery engineering equation however model selection noise science sensitivity stat.ml stemming type work