Adaptive Uncertainty-Penalized Model Selection for Data-Driven PDE Discovery
Pongpisit Thanasutives,
Takashi Morita,
Masayuki Numao
et al.
Abstract:We propose a new parameter-adaptive uncertainty-penalized Bayesian information criterion (UBIC) to discover the stable governing partial differential equation (PDE) composed of a few important terms. Since the naive use of the BIC for model selection yields an overfitted PDE, the UBIC penalizes the found PDE not only by its complexity but also by its quantified uncertainty. Representing the PDE as the best subset of a few candidate terms, we use Bayesian regression to compute the coefficient of variation (CV) … Show more
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