Description
Quantitative and lightweight prediction of turbulent transport and profile formation has an important role in the fusion plasmas. To this end, some integrated simulation code which use reduced model and machine learning prediction has been developed. However, these predictions are too simplified and often have limitations in sufficiently capture the nonlinearities of turbulent transport.
We have developed a global transport co-simulation AGITO (Alterable Gyrokinetics–Integrated Transport cO–simulation) [1], formerly called TRESS+GKV. AGITO uses Multiple Program Multiple Data (MPMD) parallelization to directly couple discretely distributed local gyrokinetic simulations (GKV) with a one-dimensional radial transport solver (TRESS), which calculates the time evolution of pressure and plasma current profiles.
Turbulent transport can be efficiently evaluated using simplified models that include nonlinear effects of zonal flows [2]. This model allows a reduction in computational cost to approximately 1/200 , while linear gyrokinetic calculations are still required at all time steps. In this study, a Gaussian process (GP) model is introduced into AGITO to further reduce the computational cost. The GP model is constructed using gyrokinetic simulation results obtained during the initial few time steps at each radial position as training data.
If the variance of the value predicted by the GP model is below a specified threshold, TRESS uses the predicted value as the turbulent diffusivity. Conversely, when the variance exceeds the threshold, a gyrokinetic simulation is performed to reevaluate the turbulent transport and to update the GP model by adding new training data.
Predicting nonlinear behavior, such as turbulent transport near marginal gradients, using GP models is generally challenging. For this issue, heteroscedastic Gaussian process [3] regression is introduced. In this study, the intensity ratio of zonal flow is treated as a heteroscedastic noise term. This approach enables stable prediction of turbulent transport near marginal gradients, which is difficult to achieve with conventional GP models.
[1] T. Nakayama, et al., Plasma Physics and Controlled Fusion 67.10 (2025): 105012
[2] T. Nakayama, et al., Scientific Reports 13.1 (2023): 2319.
[3] P. Goldberg, et al., Advances in neural information processing systems 10 (1997).