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.

中文翻译：

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一种高斯矩方法及其通过 LSTM 递归神经网络的增强用于空泡种群统计

相平均稀气泡流模型需要气泡群的高阶统计矩。直接在概率空间中演化气泡箱的分类方法是准确的，但计算成本很高。基于高斯闭包的基于矩的方法提供了加速这种方法的机会，特别是当气泡尺寸分布很宽（多分散）时。对于线性气泡动力学，高斯闭包是精确的，但对于经历大的非线性振荡的气泡，它会因高阶矩的错误表示而导致很大的误差。提出了在蒙特卡罗真实数据上训练的长短期记忆循环神经网络来改进这些模型预测。该网络用于校正低阶矩演化方程并基于低阶矩改进对高阶矩的预测。结果表明，网络可以将模型错误减少到低于其未增强值的 1% 美元。