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.

通过学习和演变系统的有效动力学，我们引入生成模型来加速复杂系统的模拟。在提出的 G-LED 中，高维数据的实例被降采样到一个更低维度的流形中，并通过自回归注意机制进行演变。反过来，贝叶斯扩散模型将这个低维流形映射到相应的高维空间，捕捉系统动力学的统计特性。我们在几个基准系统的模拟中展示了 G-LED 的能力和局限性，包括 Kuramoto-Sivashinsky（KS）方程、反向阶梯上的二维高雷诺数流动和三维湍流通道流的模拟。结果表明，生成学习为以更低的计算成本准确预测复杂系统的统计特性开辟了新的前沿。