用生成对抗网络预测可变参数下的流体动态，精度高且能自动学习参数依赖关系。
Data-driven Modeling of Parameterized Nonlinear Fluid Dynamical Systems with a Dynamics-embedded Conditional Generative Adversarial Network
- 在条件GAN中嵌入动力学模块，同时学习时间演化与参数影响。
- 在不同雷诺数下对圆柱绕流和腔体流模拟，预测误差低且稳定。
- 发现训练时长存在最优值，由误差和互信息共同决定。
本文提出一种数据驱动方法，利用嵌入动力学模块的条件生成对抗网络（Dyn-cGAN）作为代理模型，精准预测具有参数化的非线性流体动力系统。该模型通过改进的条件GAN结构，实现对时间演化规律及其对系统参数依赖关系的联合识别。所学得的Dyn-cGAN模型可依据输入参数准确预测系统流场。我们在多个参数化非线性流体系统上评估了该方法的有效性与局限性，包括不同雷诺数下的圆柱绕流和二维腔体问题。进一步研究了雷诺数对预测精度的影响，并探究了动力学模块训练中时间步数对预测准确性的影响，发现存在一个最优时间步数，其选择基于与真实数据的误差及互信息水平。
原文摘要 · Abstract (English)
This work presents a data-driven solution to accurately predict parameterized nonlinear fluid dynamical systems using a dynamics-generator conditional GAN (Dyn-cGAN) as a surrogate model. The Dyn-cGAN includes a dynamics block within a modified conditional GAN, enabling the simultaneous identification of temporal dynamics and their dependence on system parameters. The learned Dyn-cGAN model takes into account the system parameters to predict the flow fields of the system accurately. We evaluate the effectiveness and limitations of the developed Dyn-cGAN through numerical studies of various parameterized nonlinear fluid dynamical systems, including flow over a cylinder and a 2-D cavity problem, with different Reynolds numbers. Furthermore, we examine how Reynolds number affects the accuracy of the predictions for both case studies. Additionally, we investigate the impact of the number of time steps involved in the process of dynamics block training on the accuracy of predictions, and we find that an optimal value exists based on errors and mutual information relative to the ground truth.
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