  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.
