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

Spencer H Bryngelson, Alexis-Tzianni Charalampopoulos, Themistoklis Sapsis, Tim Colonius

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 higherorder 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.