用神经网络模拟托卡马克等离子体形状控制,实现毫秒级实时响应。
Real-Time Applicability of Emulated Virtual Circuits for Tokamak Plasma Shape Control
- 用约10^5参数的神经网络模拟形状敏感矩阵,替代传统计算方法。
- 在10^5~10^6个合成平衡态上训练后,误差控制在5%-10%以内。
- 通过线性回归从线圈电流推算未测舱体电流,精度达几安培。
机器学习最近被用于模拟托卡马克等离子体磁控中的敏感度矩阵以实现实时控制。然而,此类方法仍需量化潜在误差。本文报告了模拟器在实时应用中的两个方面:首先,通过形状模拟器雅可比矩阵计算的目标位移与基于精确Grad-Shafranov解的有限差分雅可比矩阵结果相比,对选定几何目标可达到约5%-10%的吻合度;使用约10^5参数的神经网络模型,并在约10^5-10^6个合成平衡态上训练,可避免过正则化或过拟合。在特定形状目标上训练的小型模型还可进一步微调以更好匹配雅可比矩阵。其次,针对未实时测量的舱体电流,通常被归入“成形电流”进行虚拟电路设计。本文证明,通过在活动线圈电流的滑动窗口上进行简单线性回归,可推算出成形电流,残差仅几安培,从而在每个放电时刻选择最合适的成形电流。这些结果基于面向MAST-U的历史放电数据和仿真,表明可在现有及未来托卡马克中开发出延迟仅为几毫秒的稳健实时等离子体形状控制模拟器。
原文摘要 · Abstract (English)
Machine learning has recently been adopted to emulate sensitivity matrices for real-time magnetic control of tokamak plasmas. However, these approaches would benefit from a quantification of possible inaccuracies. We report on two aspects of real-time applicability of emulators. First, we quantify the agreement of target displacement from VCs computed via Jacobians of the shape emulators with those from finite differences Jacobians on exact Grad-Shafranov solutions. Good agreement ($\approx$5-10%) can be achieved on a selection of geometric targets using combinations of neural network emulators with $\approx10^5$ parameters. A sample of $\approx10^{5}-10^{6}$ synthetic equilibria is essential to train emulators that are not over-regularised or overfitting. Smaller models trained on the shape targets may be further fine-tuned to better fit the Jacobians. Second, we address the effect of vessel currents that are not directly measured in real-time and are typically subsumed into effective "shaping currents" when designing virtual circuits. We demonstrate that shaping currents can be inferred via simple linear regression on a trailing window of active coil current measurements with residuals of only a few Ampères, enabling a choice for the most appropriate shaping currents at any point in a shot. While these results are based on historic shot data and simulations tailored to MAST-U, they indicate that emulators with few-millisecond latency can be developed for robust real-time plasma shape control in existing and upcoming tokamaks.
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