Statistical Uncertainty Quantification of Gyrokinetic Turbulence Simulation Fluxes

Gyrokinetic theory has emerged as the cornerstone for understanding turbulent transport in magnetically confined plasmas, such as those found in tokamaks and stellarators. Accurate and reliable quantification of turbulent transport fluxes is critical for gyrokinetic simulations that guide fusion device design, modeling and optimization. Traditionally, these fluxes are estimated from single, computationally demanding, long-duration simulations. However, such approaches suffer from slow convergence, large variance, transient contamination, and strong autocorrelation, complicating uncertainty quantification (UQ) and reducing confidence in predictions.

In this work, we propose and validate an ensemble-based statistical framework leveraging multiple shorter gyrokinetic simulation runs, each initiated with slightly perturbed random seeds. By integrating time-series diagnostics, steady-state detection algorithms, and short-term averaging using sliding and non-overlapping window methods, our methodology identifies statistically steady regions and provides uncertainty estimates. We further incorporate effective sample size corrections and autocorrelation-aware estimators to address temporal dependence within the data. Our results confirm that ensemble-based analysis offers a scalable and computationally efficient alternative to traditional single-run averaging, thus enhancing confidence and reliability in gyrokinetic turbulence modeling outcomes for fusion energy research.