Fusion energy research is being pursued around the world as a means of solving energy problems. Magnetic confinement fusion reactors aim to extract fusion energy by confining extremely hot plasma in strong magnetic fields. Its development is a comprehensive engineering project involving many advanced technologies, such as superconducting magnets, reduced-activation materials, and beam and wave heating devices. In addition, predicting and controlling the confined plasma, in which numerous charged particles and electromagnetic fields interact in complex ways, is an interesting research subject from a physics perspective.
To understand the transport of energy and particles in confined plasmas, theoretical studies, numerical simulations using supercomputers, and experimental measurements of plasma turbulence are being conducted. Although physics-based numerical simulations can predict turbulent transport in plasmas and agree with experimental observation to some extent, there are sometimes deviations from experiments. Therefore, the quantitative reliability of the predictions remains an issue. On the other hand, empirical prediction models based on experimental data have been developed. Still, it is uncertain whether they can be applied to future experimental devices based only on data obtained from existing experimental devices. Thus, theory/simulation and experimental data each have advantages and disadvantages, and there are areas where one alone cannot fully compensate for the other. If there is plenty of data with enough accuracy, it is possible to create turbulent transport models through machine learning, such as neural networks. However, to predict future nuclear fusion burning plasmas that have not yet been realized, the data is often lacking; either less quantitatively or in an insufficient amount to cover the parameter range of interest.
To solve this problem, we have adopted the concept of multi-fidelity modeling that enhances the predictive accuracy of the limited number of highly accurate (high-fidelity) data. To compensate for the lack of high-fidelity data, one uses less accurate but more numerous low-fidelity data. This study introduces a multi-fidelity data fusion method called nonlinear auto-regressive Gaussian process regression (NARGP) to turbulent transport modeling in plasmas. In a conventional regression problem, a single pair of input and output data is given as a set, and a regression model is built based on the pair. However, a multi-fidelity problem has multiple outputs with different fidelities for the same input. The idea of NARGP is to express the prediction of high-fidelity data as a function of input and low-fidelity data. It is demonstrated that the multi-fidelity data fusion method improves the prediction accuracy of plasma turbulent transport models by applying the technique to cases such as (i) integration of low- and high-resolution simulation data, (ii) prediction of a turbulent diffusion coefficient based on an experimental fusion plasma data set, and (iii) integration of simplified theoretical models and turbulence simulation data. By incorporating the physical model-based predictability of theory and simulation as low-fidelity data, the lack of quantitative experimental data that we want to predict as the high-fidelity type can be compensated for improving prediction accuracy. These results have been published in a journal of the Nature publishing group, Scientific Reports.
Until now, turbulent transport modeling research has been dominated by two approaches: one pursuing predictions based on physical models from theory and simulation and the other constructing empirical models to fit existing experimental data. The present research paves the way to a new method that combines the best of both approaches: the predictability of theory and simulation based on physical models, and the quantitative information obtained from experimental data. By doing so, we are attempting to realize a prediction method for future nuclear fusion burning plasmas that combines the knowledge of simulations with the accuracy of experimental data.
The multi-fidelity modeling approach can be applied to various multi-fidelity data, including simulation and experimental data, simplified theory and simulation, and low- and high-accuracy simulations. Therefore, it is expected to be applied not only to fusion plasma research but also to other fields as a general method to construct fast and accurate prediction models by using a small number of high-precision data. It will contribute to performance prediction and design optimization of fusion reactors and develop new technologies in other fields.
