NTVTOK-ML: Fast surrogate model for neoclassical toroidal viscosity torque calculation in tokamaks based on machine learning methods

The Neoclassical Toroidal Viscosity (NTV) torque is a crucial source of toroidal momentum in tokamaks, exerting significant influence on plasma instability and performance. Accurate numerical modeling of NTV torque is essential for experimental design and operation, as well as for gaining insight into the relevant physical processes. However, the time-consuming nature of NTV torque calculation poses challenges for its practical application in experiment analysis and physical investigations. In this study, we have developed NTVTOK-ML, a surrogate model for NTV torque calculation that combines the expressive power and fast inference of machine learning methods to achieve simultaneous accuracy and time efficiency. To obtain datasets for NTV torque, extensive numerical calculations using NTVTOK and MARS-F codes were performed under various plasma conditions of Experimental Advanced Superconducting Tokamak (EAST), covering a wide range of experimentally relevant parameter regimes and incorporating rich physical effects such as pitch angle scattering, full toroidal geometry, resonances, etc. For fixed magnetic perturbation case, NTVTOK-ML employs Multi-Layer Perceptron (MLP) deep neural network and eXtreme Gradient Boosting (XGBoost) ensemble learning techniques respectively. Furthermore, when considering linear plasma response effect, Convolutional Neural Network (CNN) is utilized to process two-dimensional magnetic perturbation data. The prediction accuracy of NTVTOK-ML is evaluated based on statistical metrics including coefficient of determination (R^2), mean squared error (MSE), and relative error; single sample prediction ability; and generalization ability - demonstrating its reliability in NTV torque prediction tasks. Importantly, the computational time required for predicting NTV torque using our proposed approach is significantly reduced compared to the original numerical code by several orders of magnitude. Additionally, the flexibility offered by the NTVTOK-ML framework allows users to optimize model performance under specific circumstances. Overall, our developed method provides an accessible solution for rapid yet accurate prediction of NTV torque while incorporating essential physical effects - thereby facilitating real-time or inter-shot analysis in experiments as well as comprehensive multi-scale nonlinear time evolution modeling.

新古典主义环状粘度（NTV）扭矩是托卡马克中环向动量的重要来源，对等离子体不稳定性及性能产生显著影响。精确的NTV扭矩数值模拟对于实验设计、操作以及深入了解相关物理过程至关重要。然而，NTV扭矩计算的耗时特性给其实际应用于实验分析和物理研究中带来了挑战。在本研究中，我们开发了NTVTOK-ML，这是一种用于NTV扭矩计算的代理模型，它结合了机器学习方法的表达能力和快速推理，以实现准确性与时间效率的同步提升。为了获取NTV扭矩数据集，我们利用NTVTOK和MARS-F代码在实验先进超导托卡马克（EAST）的多种等离子体条件下进行了广泛的数值计算，涵盖了广泛的实验相关参数范围，并纳入了诸如散度角散射、全环向几何、共振等丰富的物理效应。对于固定磁场扰动情况，NTVTOK-ML分别采用多层感知器（MLP）深度神经网络和极端梯度提升（XGBoost）集成学习技术。此外，在考虑线性等离子体响应效应时，利用卷积神经网络（CNN）处理二维磁场扰动数据。NTVTOK-ML的预测精度基于统计指标进行评估，包括决定系数（R^2）、均方误差（MSE）和相对误差；单样本预测能力；以及泛化能力——展示了其在NTV扭矩预测任务中的可靠性。重要的是，使用我们提出的方法预测NTV扭矩所需的计算时间与原始数值代码相比降低了几个数量级。此外，NTVTOK-ML框架的灵活性使用户能够在特定情况下优化模型性能。总体而言，我们开发的方法为快速且准确的NTV扭矩预测提供了一种可行方案，同时纳入了必要的物理效应——从而促进了实验中的实时或跨脉冲分析以及全面的多尺度非线性时间演化建模。