用神经网络从少量传感器数据重建磁流体状态，加速核聚变模拟。
Surrogate models for nuclear fusion with parametric Shallow Recurrent Decoder Networks: applications to magnetohydrodynamics
- 结合SVD降维与浅层循环解码器，从稀疏测量数据恢复全时空状态。
- 仅用3个温度传感器输入，即可准确重构速度、压力和温度全场，磁场强度超出训练范围仍有效。
- 适合需要实时监控与控制的核聚变系统，计算成本低，鲁棒性强。
磁流体动力学（MHD）在核聚变系统的设计与运行中起关键作用，涉及导电流体（如液态金属或熔盐）与强弱及方向变化的磁场相互作用，影响流动行为。传统数值求解这类高度非线性多物理场方程组计算成本高，尤其在多查询、参数化或实时场景中。本文提出一种完全数据驱动的MHD状态重建框架，结合奇异值分解（SVD）进行降维，并采用浅层循环解码器（SHRED）神经网络，从少量观测点的时序数据中重建完整时空状态。研究以压缩式铅锂流经阶梯通道为例，考虑热梯度与宽范围磁感应强度。通过SVD压缩全阶数据集生成参考真值用于训练，仅提供3个温度传感器输入，网络可重建速度、压力与温度全场。为评估传感器布局鲁棒性，测试了30种随机配置的集成结果。结果显示，即使面对训练未覆盖的磁场强度，SHRED仍能准确重构全状态。表明该方法在融合相关多物理场问题中具备高效代理建模潜力，支持低成本状态估计，适用于实时监测与控制。
原文摘要 · Abstract (English)
Magnetohydrodynamic (MHD) effects play a key role in the design and operation of nuclear fusion systems, where electrically conducting fluids (such as liquid metals or molten salts in reactor blankets) interact with magnetic fields of varying intensity and orientation, which affect the resulting flow. The numerical resolution of MHD models involves highly nonlinear multiphysics systems of equations and can become computationally expensive, particularly in multi-query, parametric, or real-time contexts. This work investigates a fully data-driven framework for MHD state reconstruction that combines dimensionality reduction via Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED), a neural network architecture designed to recover the full spatio-temporal state from sparse time-series measurements of a limited number of observables. The methodology is applied to a parametric MHD test case involving compressible lead-lithium flow in a stepped channel subjected to thermal gradients and magnetic fields spanning a broad range of intensities. To improve efficiency, the full-order dataset is first compressed using SVD, yielding a reduced representation used as reference truth for training. Only temperature measurements from three sensors are provided as input, while the network reconstructs the full fields of velocity, pressure, and temperature. To assess robustness with respect to sensor placement, thirty randomly generated sensor configurations are tested in ensemble mode. Results show that SHRED accurately reconstructs the full MHD state even for magnetic field intensities not included in the training set. These findings demonstrate the potential of SHRED as a computationally efficient surrogate modeling strategy for fusion-relevant multiphysics problems, enabling low-cost state estimation with possible applications in real-time monitoring and control.
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