AI 中文总结
研究针对非线性物理系统瞬态到稳态模拟成本高的问题，提出在遍历性假设下直接对饱和态分布建模（GyroFlow），该方法能直接估计陀螺动力学湍流稳态统计量，优于其他方法，还能加速及用于热启动数值代码。
AI 中文摘要
许多非线性物理系统在达到统计稳态前有初始瞬态阶段，直接数值模拟成本高。计算流体动力学中，大涡模拟等降阶方法可降低成本。而在陀螺动力学等系统中，有效闭合方法难寻，现有替代建模方法有累积误差。本文提出在遍历性假设下直接对饱和态分布建模，绕过显式时间演化，引入GyroFlow，它能直接估计5维相空间中陀螺动力学湍流的稳态统计量，优于其他方法，还能加速。提出FGyD评估生成质量，且GyroFlow可用于热启动数值代码。
英文摘要
Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching it, incurring significant computational cost. In Computational Fluid Dynamics, reduced-order approaches such as Large Eddy Simulation mitigate computational cost by modeling small-scale dynamics, enabling tractable approximations of turbulent flows. In contrast, for systems such as gyrokinetics, comparably effective closures for the full dynamics are not generally available, and high-fidelity simulations remain necessary. Existing surrogate modeling approaches for these systems are autoregressive, hence they suffer from accumulating error. We instead propose to bypass explicit time evolution by directly modeling the distribution of saturated states under an ergodicity assumption, stating that ensemble averages over samples are equivalent to time averages of a single long simulation. We introduce GyroFlow, a latent generative model that directly estimates steady-state statistics of gyrokinetic turbulence in 5D phase space, without resolving the transient phase. GyroFlow generates saturated snapshots from noise, conditioned on dimensionless operating parameters and outperforms autoregressive, reduced-order, and other generative approaches, while providing substantial speedup. To evaluate generation quality we propose FGyD, a distributional metric computed in the latent space of a pretrained gyrokinetic model, and show that it correlates with downstream flux accuracy and solver convergence. Finally, GyroFlow can be used to warm-start the numerical code used to produce the data.
