用多智能体强化学习优化玻尔兹曼模拟，提升粗粒度仿真的稳定性与精度。
Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learning
- 通过卷积神经网络动态调节局部松弛参数，实现自适应闭合模型。
- 在湍流柯尔莫戈罗夫流动中稳定模拟，恢复高分辨率仿真能量谱。
- 模型可迁移至未训练场景，性能优于传统方法，适合复杂流体模拟。
格子玻尔兹曼方法（LBM）为模拟从微流体到空气动力学的多种流体现象提供了强大而灵活的工具。由于系统中存在的广泛时空尺度，完全解析的模拟目前不切实际，因此需要有效的闭合模型来处理欠分辨率的模拟。现有的欠分辨率LBM往往不稳定，尽管已有诸多努力尝试稳定它们，但通常难以跨尺度和物理系统泛化。本文提出一种新颖的数据驱动多智能体强化学习（MARL）方法，显著提升了粗粒度LBM模拟的稳定性和准确性。该方法使用卷积神经网络动态调控模拟网格上各处的局部松弛参数。在湍流柯尔莫戈罗夫流动中展示了该框架的有效性。结果表明，基于MARL的闭合模型使模拟稳定，并恢复了比全分辨率模拟成本低得多的能源谱，同时保持计算效率。所学闭合模型可迁移至训练中未见的流动场景，相比传统LBM模型具有更强的鲁棒性和光谱精度。我们相信，MARL闭合模型为高效准确模拟众多当前单一LBM方法无法触及的复杂问题开辟了新途径。
原文摘要 · Abstract (English)
The Lattice Boltzmann method (LBM) offers a powerful and versatile approach to simulating diverse hydrodynamic phenomena, spanning microfluidics to aerodynamics. The vast range of spatiotemporal scales inherent in these systems currently renders full resolution impractical, necessitating the development of effective closure models for under-resolved simulations. Under-resolved LBMs are unstable, and while there is a number of important efforts to stabilize them, they often face limitations in generalizing across scales and physical systems. We present a novel, data-driven, multiagent reinforcement learning (MARL) approach that drastically improves stability and accuracy of coarse-grained LBM simulations. The proposed method uses a convolutional neural network to dynamically control the local relaxation parameter for the LB across the simulation grid. The LB-MARL framework is showcased in turbulent Kolmogorov flows. We find that the MARL closures stabilize the simulations and recover the energy spectra of significantly more expensive fully resolved simulations while maintaining computational efficiency. The learned closure model can be transferred to flow scenarios unseen during training and has improved robustness and spectral accuracy compared to traditional LBM models. We believe that MARL closures open new frontiers for efficient and accurate simulations of a multitude of complex problems not accessible to present-day LB methods alone.
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