A Shortcut to Statistically Steady-State Turbulence with Flow Matching

2026-07-14

AI Summary

High-fidelity gyrokinetic turbulence simulations are computationally expensive due to the need to resolve the full temporal evolution from transients to statistical steady states, and efficient reduced-order models remain lacking. This work addresses this challenge by leveraging the ergodicity hypothesis to bypass explicit time integration and, for the first time, applies flow matching to directly generate steady-state statistical distributions of saturated turbulence in five-dimensional phase space. Conditioned on dimensionless operational parameters, the proposed latent-space generative model, GyroFlow, synthesizes high-quality steady-state snapshots from noise by integrating a pre-trained physics-informed metric with a conditional generation mechanism. A new evaluation metric, FGyD, is introduced to assess fidelity. Experiments demonstrate that GyroFlow outperforms existing autoregressive, reduced-order, and generative approaches in both sample quality and downstream flux prediction accuracy, significantly accelerating simulation and enabling effective hot-starting of the original solver.

Abstract

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.

Problem

• statistically steady-state turbulence
• gyrokinetics
• transient dynamics
• surrogate modeling
• computational cost

Innovation

• flow matching
• gyrokinetic turbulence
• latent generative model
• statistically steady state
• surrogate modeling