The integrated behavior of the fluid flow, encompassing variation of some specific response, has received more attention than mere examination of velocity and pressure distributions. A machine learning framework is introduced for the first time to elucidate and predict the complex fluid dynamic responses across varying time scales. For the same class of fluid processes, the dynamic response curves with varying time durations can be defined in terms of time scales and curve shapes. The former is predicted by a single-objective regression model, and the curves are normalized and recovered using time scaling and uniform interpolation. The latter are downscaled by Principal Component Analysis (PCA) and then predicted by a multi-objective regression model. As a novel application, this framework is employed to analyze small bubbles in a Newtonian fluid as they impact a horizontal wall, predicting the velocity, aspect ratio, and position dynamic response of the bubbles. Both Random Forest and Gaussian Process models, based on PCA-driven data processing, exhibit remarkable accuracy in describing and predicting complex dynamics of rising bubbles. Notably, PCA's principal components demonstrate independence and are set through rigorous cross-validation of the training set, rather than dependence on the Cumulative Variance Explained (CVE) values. Furthermore, our framework adeptly extends to predict the complex behavior of multiple bubble bounces by concatenating individual bounce predictions with high efficiency and precision. The proposed framework proves to be a catalyst for comprehending the dynamic response of fluids.

中文翻译：

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上升气泡撞击水平壁的动态响应的机器学习预测模型


流体流动的综合行为（包括某些特定响应的变化）比单纯检查速度和压力分布受到了更多关注。首次引入机器学习框架来阐明和预测不同时间尺度的复杂流体动力学响应。对于同一类流体过程，可以用时间尺度和曲线形状来定义不同持续时间的动态响应曲线。前者通过单目标回归模型进行预测，并使用时间缩放和均匀插值对曲线进行归一化和恢复。后者通过主成分分析（PCA）进行缩小，然后通过多目标回归模型进行预测。作为一种新颖的应用，该框架用于分析牛顿流体中的小气泡撞击水平壁时的情况，预测气泡的速度、纵横比和位置动态响应。基于 PCA 驱动的数据处理的随机森林和高斯过程模型在描述和预测上升气泡的复杂动态方面表现出极高的准确性。值得注意的是，PCA 的主要组成部分表现出独立性，并且是通过训练集的严格交叉验证来设置的，而不是依赖于累积方差解释 (CVE) 值。此外，我们的框架通过高效率和高精度连接单个反弹预测，巧妙地扩展到预测多个气泡反弹的复杂行为。所提出的框架被证明是理解流体动态响应的催化剂。