A Bayesian Framework for learning governing Partial Differential Equation from Data
Abstract
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to note that existing methods often struggle to identify the underlying equation accurately in the presence of noise. In this study, we present a new approach to discovering PDEs by combining variational Bayes and sparse linear regression. The problem of PDE discovery has been posed as a problem to learn relevant basis from a predefined dictionary of basis functions. To accelerate the overall process, a variational Bayes-based approach for discovering partial differential equations is proposed. To ensure sparsity, we employ a spike and slab prior. We illustrate the efficacy of our strategy in several examples, including Burgers, Korteweg-de Vries, Kuramoto Sivashinsky, wave equation, and heat equation (1D as well as 2D). Our method offers a promising avenue for discovering PDEs from data and has potential applications in fields such as physics, engineering, and biology.
Cite
@article{arxiv.2306.04894,
title = {A Bayesian Framework for learning governing Partial Differential Equation from Data},
author = {Kalpesh More and Tapas Tripura and Rajdip Nayek and Souvik Chakraborty},
journal= {arXiv preprint arXiv:2306.04894},
year = {2023}
}