基于神经网络的托卡马克能量约束时间预测

doi:10.19596/j.cnki.1001-246x.8277

摘要/Abstract

摘要：

使用机器学习理论中的神经网络方法，根据通用逼近原理对能量约束时间的复杂函数进行逼近，采用托卡马克装置的典型实验数据，设计一种组合结构的神经网络。通过大量的调参试验，给出一套性能最好的参数组合，并与传统幂指数形式的多元线性回归方法进行准确性和数据集迁移能力的比较。结果表明：神经网络模型对于能量约束时间的预测准确率更高，回归性能更好，且具有一定的抗噪声能力，更适合作为能量约束时间的定标或预测工具。

关键词: 托卡马克, 能量约束时间, 神经网络

Abstract:

A neural network method in machine learning theory is used to approximate complex function of energy confinement time in tokamak according to the general approximation principle. A combined structure neural network is designed based on typical experimental data of domestic tokamak. Though a series of parameter adjustment tests, a set of parameters with best performance is obtained. Energy confinement times calculated with neural network model are compared with those by power exponential multiple linear regression. It shows that the neural network model has better accuracy and prediction performance. Noise resistance experiments show that the neural network model has certain anti-noise ability. Therefore, neural network is a favorable candidate for calibration or prediction of energy confinement time.

Key words: tokamak, energy confinement time, neural network

中图分类号:

O532⁺.1

郑书昱, 彭佳臻, 张先梅, 薛二兵, 虞立敏. 基于神经网络的托卡马克能量约束时间预测[J]. 计算物理, 2021, 38(4): 423-430.

Shuyu ZHENG, Jiazhen PENG, Xianmei ZHANG, Erbing XUE, Limin YU. Prediction of Energy Confinement Time in Tokamak Based on Neural Networks[J]. Chinese Journal of Computational Physics, 2021, 38(4): 423-430.

图/表 10

图1 放电稳定阶段的等离子体电流

Fig.1 Experimental plasma current during steady state of discharge

图2 多层感知机结构

Fig.2 Structure of a multilayer perception

图3 组合网络结构

Fig.3 Structure of a composite network

图4 组合网络与仅浅层网络预测值的残差

Fig.4 Residuals of predicted values of composite networks and shallow networks

表1 网络中各项参数的数值

Table 1 Values of parameters in the network

学习率	优化器	学习率衰减	Batch size	正则化系数
3×10^-4	ADAM(0.9, 0.96)	0.994	0.235	0.002

表2 多元线性回归模型与神经网络模型性能比较

Table 2 Performance of multiple regression model and neural network model

	e_RMSE	e_MAPE/%	R²
多元线性回归	0.011	17.104	0.335
神经网络模型	0.007	12.194	0.729

图5 整体数据集上多元线性回归与神经网络模型给出的能量约束时间

Fig.5 Energy confinement times with multiple regression model and neural network model in total sets

表3 多元线性回归模型与神经网络模型在测试集上的比较

Table 3 Performance of multiple regression model and neural network model in testing sets

	e_RMSE	e_MAPE/%	R²
多元线性回归	0.022	20.869	0.149
神经网络模型	0.010	13.518	0.574

图6 测试集中多元线性回归与神经网络模型给出的能量约束时间

Fig.6 Energy confinement times with multiple regression model and neural network model in testing sets

表4 神经网络模型抵抗噪声的能力

Table 4 Resistance to noise of the neural network model

噪声数据比例/%	e_RMSE	e_MAPE/%	R²
0	0.010	13.518	0.574
5	0.013	13.741	0.562
10	0.013	13.852	0.519

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