7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Convolutional neural network models for forecasting heat fluxes calculated by
nonlinear gyrokinetic simulations
E. Narita1, M. Honda1, S. Maeyama2 and T.-H. Watanabe2
1
Graduate School of Engineering, Kyoto University,
2
Graduate School of Science, Nagoya University
e-mail (speaker): narita.emi.5s@kyoto-u.ac.jp
Nonlinear gyrokinetic simulations are performed tocalculate heat and particle fluxes caused by turbulent
fluctuations in fusion plasmas. In such simulations, thetime evolution of the perturbed distribution function 𝑓"
is solved in the five-dimensional phase space. The fluxes
required for transport study are estimated in thesaturation phase that follows the growing phase. Acalculation including the growing and saturation phases
takes a few days or more on supercomputers, and thegrowing phase can consume about one-third of thecomputational resources. We have developed machinelearning based models that investigate processes leading
to turbulent saturation using data provided in thegrowing phase, aiming to infer the fluxes in thesaturation phase with a low computational cost.
We first visualized 𝑓" calculated by the flux-tube
gyrokinetic code GKV [1] in the wavenumber-space#𝑘! , 𝑘" & as shown in the image placed on the left side offigure 1. Such images are generated at every calculation
time step. Next, we constructed a convolutional neuralnetwork (CNN) model that reads the image and predicts
the simulation time at which the image was processed [2].
The CNN model was built by employing transfer
learning and fine-tuning techniques based on theEfficientNet-B4 [3], which is a state-of-the-art CNN
model trained on a huge number of real-world images.
The simulation time predicted by the CNN model can beconverted into the time when the saturation phasecommences. The saturation time changes due to theinitial condition and an early saturation time is desirable
for an effective use of the computational resources. We
can utilize the CNN model to optimize the initialcondition by forecasting the saturation time.
Our first CNN model was unable to predict fluxes#since the images fed into the model show '𝑓"'normalized with the maximum value at each time and donot provide information on the fluctuation amplitude tothe model. To extend the capability of the model, wehave developed a multimodal model, adding the#magnitude of the electrostatic potential '𝜙)' as an input
parameter as shown in figure 1. The image and the value#of '𝜙)' are handled by the CNN and the multilayer
perceptron, respectively, and the generated feature
vectors are concatenated to forecast the simulation time
and the electron and ion heat fluxes. The multimodal
CNN model was trained on data produced by thesimulation for the Cyclone base case (CBC), which is ade facto standard DIII-D parameter set for the

gyrokinetic simulation benchmarking test. When theCBC-based predictor is applied to the simulation for aJT-60U plasma parameter set, it successfully forecasts
the heat fluxes as well as the simulation time as shown infigure 2 [4]. Such high predictability can be attributed to
the fact that turbulence of both the CBC and the JT-60U
case is dominantly driven by the ion temperature
gradient mode/trapped electron mode. If a test case hasother dominant instability, a predictor trained on theequivalent case should be applied.
To forecast fluxes ahead of the input image and value,
an extended model including a recurrent NN is underdevelopment. The preliminary model shows the ability toinfer the saturated heat flux from data given in thegrowing phase, and it could cut the computational costby about half.

Figure 1 Architecture of the multimodal CNN model.

Figure 2 Regression plots of the predicted (a) simulation
time and (b) electron and (c) ion heat fluxes against thetrue values for test data. The determination coefficients
𝑅# are embedded in the plots.
References[1] T.-H. Watanabe and H. Sugama, Nucl. Fusion, 4624 (2006).
[2] E. Narita, M. Honda, S. Maeyama and T.-H.
Watanabe, Nucl. Fusion, 62 086037 (2022).
[3] M. Tan and Q. V. Le, arXiv: 1905.11946 (2019).
[4] M. Honda, E. Narita, S. Maeyama and T.-H.
Watanabe, Contrib. Plasma Phys., e202200137(2023).