液滴动力学中的能量预算预测：一种循环神经网络方法
Predicting Energy Budgets in Droplet Dynamics: A Recurrent Neural Network Approach
AI总结：
本研究提出一种基于LSTM的循环神经网络方法，利用几何时间序列数据预测液滴动力学中的能量预算（动能、耗散能和表面能），并在多种雷诺数和韦伯数下验证了准确性，同时探索了用几何数据估计静态参数的可能性。
摘要：
神经网络在流体力学中提供了一种探索复杂流动（包括多相流和自由表面流）的高效方法。循环神经网络，特别是长短期记忆（LSTM）模型，在从瞬态输入学习到动态输出的映射方面表现出吸引力。本研究将LSTM应用于预测表面张力效应下流体流动的瞬态和静态输出。具体而言，我们探索了两种不同的液滴动力学场景：具有不同初始形状的液滴撞击固体表面，以及两个液滴碰撞后的聚结。仅使用无量纲数和数值模拟中的几何时间序列数据，LSTM即可预测能量预算。采用标记-单元前跟踪方法与标记-单元有限差分策略相结合来模拟液滴动力学。使用以几何参数（例如液滴直径变化）导出的时间序列数据输入的循环神经网络（RNN）架构，我们的研究展示了该方法在预测液滴动力学问题中跨一系列雷诺数和韦伯数的能量预算（如动能、耗散能和表面能趋势）方面的准确性。最后，采用一种仅使用几何数据（在实验环境中易于获取）的两阶段顺序神经网络来预测能量，并利用这些能量估计静态参数，如雷诺数和韦伯数。虽然我们的方法主要基于模拟数据进行了验证，但其对实验数据集的适应性是未来探索的一个有前景的方向。我们希望我们的策略能适用于多种应用，从喷墨打印到内燃机，在这些应用中，能量预算或耗散能的预测至关重要。
英文摘要：
Neural networks in fluid mechanics offer an efficient approach for exploring complex flows, including multiphase and free surface flows. The recurrent neural network, particularly the Long Short-Term Memory (LSTM) model, proves attractive for learning mappings from transient inputs to dynamic outputs. This study applies LSTM to predict transient and static outputs for fluid flows under surface tension effects. Specifically, we explore two distinct droplet dynamic scenarios: droplets with diverse initial shapes impacting with solid surfaces, as well as the coalescence of two droplets following collision. Using only dimensionless numbers and geometric time series data from numerical simulations, LSTM predicts the energy budget. The marker-and-cell front-tracking methodology combined with a marker-and-cell finite-difference strategy is adopted for simulating the droplet dynamics. Using a recurrent neural network (RNN) architecture fed with time series data derived from geometrical parameters, as for example droplet diameter variation, our study shows the accuracy of our approach in predicting energy budgets, as for instance the kinetic, dissipation, and surface energy trends, across a range of Reynolds and Weber numbers in droplet dynamic problems. Finally, a two-phase sequential neural network using only geometric data, which is readily available in experimental settings, is employed to predict the energies and then use them to estimate static parameters, such as the Reynolds and Weber numbers. While our methodology has been primarily validated with simulation data, its adaptability to experimental datasets is a promising avenue for future exploration. We hope that our strategy can be useful for diverse applications, spanning from inkjet printing to combustion engines, where the prediction of energy budgets or dissipation energies is crucial.
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