Application of Neural Ordinary Differential Equations for Tokamak Plasma Dynamics Analysis

Abstract

In the quest for controlled thermonuclear fusion, tokamaks present complex challenges in understanding burning plasma dynamics. This study introduces a multi-region multi-timescale transport model, employing Neural Ordinary Differential Equations (Neural ODEs) to simulate the intricate energy transfer processes within tokamaks. Our methodology leverages Neural ODEs for the numerical derivation of diffusivity parameters from DIII-D tokamak experimental data, enabling the precise modeling of energy interactions between electrons and ions across various regions, including the core, edge, and scrape-off layer. These regions are conceptualized as distinct nodes, capturing the critical timescales of radiation and transport processes essential for efficient tokamak operation. Validation against DIII-D plasmas under various auxiliary heating conditions demonstrates the model's effectiveness, ultimately shedding light on ways to enhance tokamak performance with deep learning.

Figures (10)

• Figure 1: Multinodal model representation of tokamak plasma regions, where the left figure shows the cross section of a DIII-D plasma, and the right figure is the simplified geometry for the multinodal model.
• Figure 2: Computational framework diagram, including cylinders as datasets, squares as modules, solid lines as forward flows, and dashed lines as back propagation processes.
• Figure 3: Signals of shot 131190, including (from top to bottom, left to right) plasma current $I_P$ , toroidal magnetic field $B_0$, safety factor $q_{95}$, gas puffing rate $\mathop{}\!\text{GAS}$, ohmic heating power $P_{\Omega}$, neutral beam injection (NBI) power $P_{\mathop{}\!\text{NBI}}$, electron cyclotron heating (ECH) power $P_{\mathop{}\!\text{ECH}}$, and ion cyclotron heating (ICH) power $P_{\mathop{}\!\text{ICH}}$.
• Figure 4: Simulation results of shot 131190 core node from both the original and optimized diffusivity models, where $\hat{n}_{\sigma}^{\mathop{}\!\text{node}}$ and $\hat{T}_{\sigma}^{\mathop{}\!\text{node}}$ are from the simulations of the multinodal model, and $n_{\sigma}^{\mathop{}\!\text{node}}$ and $T_{\sigma}^{\mathop{}\!\text{node}}$ are from the experiment measurements.
• Figure 5: Simulation results of shot 131190 edge node from both the original and optimized diffusivity models, where $\hat{n}_{\sigma}^{\mathop{}\!\text{node}}$ and $\hat{T}_{\sigma}^{\mathop{}\!\text{node}}$ are from the simulations of the multinodal model, and $n_{\sigma}^{\mathop{}\!\text{node}}$ and $T_{\sigma}^{\mathop{}\!\text{node}}$ are from the experiment measurements.