Physics-informed machine learning algorithms increasingly rely on methods that balance interpretability, predictive accuracy, and computational efficiency. This paper highlights the central role of differential equation discovery, particularly of ensembles of equations, in understanding and improving learned dynamics. Using ensembles, we discover the uncertainty in the governing equations to describe complex dynamical systems. To further refine this understanding, we consider simple ensembles that could be considered as a special case of stochastic differential equations (SDEs) and more complex ensembles built with the Bayesian Network. We use Sobol indices to assess the influence of conditional distributions and thus the impact of a more sophisticated ensembling approach.

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On the Impact of Conditional Distribution in Discovered Differential Equation Ensembles

  • Xeniya Bashkova,
  • Alexander Hvatov

摘要

Physics-informed machine learning algorithms increasingly rely on methods that balance interpretability, predictive accuracy, and computational efficiency. This paper highlights the central role of differential equation discovery, particularly of ensembles of equations, in understanding and improving learned dynamics. Using ensembles, we discover the uncertainty in the governing equations to describe complex dynamical systems. To further refine this understanding, we consider simple ensembles that could be considered as a special case of stochastic differential equations (SDEs) and more complex ensembles built with the Bayesian Network. We use Sobol indices to assess the influence of conditional distributions and thus the impact of a more sophisticated ensembling approach.