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Phase-averaged dilute bubbly flow models require high-order statisticalmoments of the bubble population. The method of classes, which directly evolvebins of bubbles in the probability space, are accurate but computationallyexpensive. Moment-based methods based upon a Gaussian closure present anopportunity to accelerate this approach, particularly when the bubble sizedistributions are broad (polydisperse). For linear bubble dynamics a Gaussianclosure is exact, but for bubbles undergoing large and nonlinear oscillations,it results in a large error from misrepresented higher-order moments. Longshort-term memory recurrent neural networks, trained on Monte Carlo truth data,are proposed to improve these model predictions. The networks are used tocorrect the low-order moment evolution equations and improve prediction ofhigher-order moments based upon the low-order ones. Results show that thenetworks can reduce model errors to less than $1\%$ of their unaugmentedvalues.

A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations