We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are down sampled to a lower dimensional manifold that is evolved through an auto-regressive attention mechanism. In turn, Bayesian diffusion models, that map this low-dimensional manifold onto its corresponding high-dimensional space, capture the statistics of the system dynamics. We demonstrate the capabilities and drawbacks of G-LED in simulations of several benchmark systems, including the Kuramoto-Sivashinsky (KS) equation, two-dimensional high Reynolds number flow over a backward-facing step, and simulations of three-dimensional turbulent channel flow. The results demonstrate that generative learning offers new frontiers for the accurate forecasting of the statistical properties of complex systems at a reduced computational cost.

翻译：我们引入生成模型，通过学习和演化复杂系统的有效动力学来加速其模拟。在提出的有效动力学生成式学习（G-LED）中，高维数据实例被降采样到低维流形，并通过自回归注意力机制进行演化。随后，贝叶斯扩散模型将该低维流形映射到对应的高维空间，进而捕获系统动力学的统计特性。我们通过多个基准系统的模拟展示了G-LED的能力与局限性，包括Kuramoto-Sivashinsky（KS）方程、二维高雷诺数后向台阶流动，以及三维湍流槽道流动的模拟。结果表明，生成式学习为以降低的计算成本准确预测复杂系统的统计特性开辟了新前沿。