A Bayesian Framework for learning governing Partial Differential Equation from Data

• URL: http://arxiv.org/abs/2306.04894v1
• Date: Thu, 8 Jun 2023 02:48:37 GMT
• Title: A Bayesian Framework for learning governing Partial Differential Equation from Data
• Authors: Kalpesh More and Tapas Tripura and Rajdip Nayek and Souvik Chakraborty
• Abstract summary: We present a new approach to discovering partial differential equations (PDEs) by combining variational Bayes and sparse linear regression. Our method offers a promising avenue for discovering PDEs from data and has potential applications in fields such as physics, engineering, and biology.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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