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- W4380136238 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." @default.
- W4380136238 created "2023-06-10" @default.
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- W4380136238 date "2023-06-07" @default.
- W4380136238 modified "2023-09-27" @default.
- W4380136238 title "A Bayesian Framework for learning governing Partial Differential Equation from Data" @default.
- W4380136238 doi "https://doi.org/10.48550/arxiv.2306.04894" @default.
- W4380136238 hasPublicationYear "2023" @default.
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