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

TL;DR

This paper introduces a hybrid approach combining Gaussian moment methods with LSTM neural networks to accurately predict the statistical moments of cavitating bubble populations, especially under nonlinear oscillations, reducing errors significantly.

Contribution

It proposes augmenting Gaussian closure models with LSTM neural networks trained on Monte Carlo data to improve accuracy in nonlinear bubble dynamics modeling.

Findings

Neural networks reduce model errors to less than 1%.

Gaussian closure is exact for linear bubble dynamics.

Augmentation improves prediction of higher-order moments.

Abstract

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