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Bayesian Model Selection for Variable-coefficient Partial Differential Equation Discovery
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DOI：10.1016/j.rineng.2025.106930.png)
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Abstract
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• Data-driven discovery of parametric partial differential equations (PDEs), whose coefficients vary in either time or space, is demonstrated using Bayesian model selection. • Bayesian model selection in this paper includes extensions of the uncertainty-penalized Bayesian information criterion and Bayesian model evidence for parametric PDE discovery. • The extended uncertainty-penalized Bayesian information criterion and the extended Bayesian model evidence enable successful data-driven discovery of parametric PDEs by quantifying PDE uncertainty and appropriately selecting relevant parameters of the sparsifying prior, respectively.
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