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.

新经典环向粘滞（Neoclassical Toroidal Viscosity，NTV）力矩是托卡马克装置中环向动量的关键来源，对等离子体不稳定性与运行性能具有显著影响。准确的NTV力矩数值建模，对于实验设计与运行、深入理解相关物理过程均至关重要。然而，NTV力矩计算耗时较长的特性，给其在实验分析与物理研究中的实际应用带来了挑战。本研究开发了NTVTOK-ML模型，这是一款用于NTV力矩计算的替代模型，结合了机器学习方法的强表达能力与快速推理特性，可同时实现高精度与计算效率。为获取NTV力矩数据集，我们针对实验先进超导托卡马克（Experimental Advanced Superconducting Tokamak，EAST）的多种等离子体工况，使用NTVTOK与MARS-F程序开展了大量数值计算，覆盖了实验中涉及的广泛参数范围，并纳入了螺距角散射、完整环向几何结构、共振效应等丰富物理过程。针对固定磁扰动场景，NTVTOK-ML分别采用了多层感知机（Multi-Layer Perceptron，MLP）深度神经网络与极限梯度提升（eXtreme Gradient Boosting，XGBoost）集成学习技术。进一步地，当考虑线性等离子体响应效应时，本研究使用卷积神经网络（Convolutional Neural Network，CNN）处理二维磁扰动数据。本研究通过决定系数（coefficient of determination，R²）、均方误差（mean squared error，MSE）与相对误差等统计指标、单样本预测能力以及泛化能力，对NTVTOK-ML的预测精度进行了评估，结果证实其在NTV力矩预测任务中具备可靠性能。值得注意的是，与原始数值程序相比，本研究所提方法的NTV力矩预测所需计算时间显著降低了数个数量级。此外，NTVTOK-ML框架具备良好的灵活性，可支持用户在特定场景下优化模型性能。总体而言，我们开发的方法为快速且精准地预测NTV力矩提供了一套易用的解决方案，同时保留了核心物理效应——这将有助于实现实验中的实时分析或放电间隙分析，并支持多尺度非线性时间演化的综合建模。