用神经网络生成连续磁约束平衡态，提升托卡马克优化效率
Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis
- 用MLP将压力倍数映射到傅里叶-泽尼克基底，实现连续平衡态求解
- 在固定边界和旋转变换下，仅变压力不变量即可生成多组平衡解
- 首次实现连续平衡分布求解，适合等离子体优化与稳定性研究
理想磁流体动力学（MHD）平衡磁场的数值计算是托卡马克优化的基础，也是求解输运或湍流等更复杂偏微分方程的起点。传统方法仅求解理想MHD方程的一个静止点，由三个不变量和求解器数值方案完全定义。本文提出首个可求解连续平衡分布的方法，固定边界和旋转变换，仅改变压力不变量。该方法通过优化多层感知机（MLP）参数，将标量压力倍数映射至傅里叶-泽尼克基底，集成于现代托卡马克平衡求解器DESC中，最小化力残差。
原文摘要 · Abstract (English)
Numerical computation of the ideal Magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated Partial Differential Equations (PDEs) like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons (MLP) that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.
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