Deep Learning Model Amplifies Plasma Predictions 1,000x

Abstract

The nonlinear collision operator consumes a significant amount of computation time in tokamak whole-volume modeling, and in current numerical methods, the computational time grows O(n2), with n representing the number of plasma species. In this study, we address the acceleration of the Fokker-Planck-Landau (FPL) collision operator using deep learning techniques. The developed FPL-net, a deep learning-based nonlinear Fokker-Planck-Landau collision operator, is a fully convolutional neural network optimized for computational speed with a compact model structure. FPL-net was trained on data representing various temperature conditions of an electron plasma on a two-dimensional velocity grid, ensuring generality. The network's training incorporated physics-informed loss functions for density, momentum, and energy moments of the plasma probability distribution function, which served as constraints, and it was trained to recursively predict two time steps, achieving robust accuracy. Notably, FPL-net demonstrated full temperature relaxation, representing the first time this has been accomplished by a deep learning-based FPL collision operator. Additional experiments with noisy inputs and extended rollouts validated the model's accuracy, which also shows over 1000x acceleration compared to traditional finite volume methods. We discuss the achieved acceleration through deep learning techniques and propose potential avenues for further enhancement and refinement in future research.

A research team, led by Professor Jimin Lee and Professor Eisung Yoon in the Department of Nuclear Engineering at UNIST has unveiled a deep learning-based approach that significantly accelerate the computation of a nonlinear Fokker-Planck-Landau (FPL) collision operator for fusion plasma.

Nuclear fusion reactors, often referred to as artificial sun, relies on maintaining a high-temperature plasma environment similar to that of the sun. In this state, matter is composed of negatively charged electrons and positively charged ions. Accurately predicting the collisions between these particles is crucial for sustaining a stable fusion reaction.

The plasma state is modeled using various mathematical frameworks, one of which is the FPL equation. The FPL equation predicts collisions between charged particles, known as Coulomb collisions. Traditionally, solving this equation involved iterative methods that required extensive computational time and resources.

The proposed FPL-net can solve the FPL equation in a single step, achieving results 1,000 times faster than previous methods with an error margin of just one-hundred-thousandth, demonstrating exceptional accuracy.

The FPL collision operation is characterized by the conservation of key physical quantities-density, momentum, and energy. The researchers enhanced model accuracy by incorporating functions that preserve these quantities during the AI learning process.

The effectiveness of the FPL-net was validated through thermal equilibrium simulations, which highlighted that accurate thermal equilibrium cannot be achieved if errors accumulate during continuous simulations.

"By utilizing deep learning on GPUs, we have reduced computation time by a factor of 1,000 compared to traditional CPU-based codes," the joint research team stated. "This advancement represents a cornerstone for digital twin technologies, enabling turbulent analysis of entire nuclear fusion reactors or replicating real Tokamaks in a virtual computing environment." A Tokamak is a specialized device designed to trap plasma.

While the current study focuses on electron plasma, the researchers noted that further research is needed to extend the applications of this model to more complex plasma environments containing various impurities.

This study received support from UNIST, the National Research Foundation of Korea (NRF), and the Korea Institute of Energy Technology Evaluation and Planning (KETEP). The findings were published in the Journal of Computational Physics on February 15, 2025.

Journal Reference

Hyeongjun Noh, Jimin Lee, and Eisung Yoon,"FPL-net: A deep learning framework for solving the nonlinear Fokker-Planck-Landau collision operator for anisotropic temperature relaxation," Journal of Computational Physics, (2025).