AI 中文总结
研究由乘性噪声驱动的二维低到高转换系统，用物理信息神经网络与矢量场分解设计损失函数的机器学习方法求解哈密顿-雅可比方程，获取系统准势等信息，相比经典模型有更易测变量和更全面物理基础，能描述托卡马克启动阶段动力学。
AI 中文摘要
本工作提出了一个二维耦合的低到高约束转换系统，其基于托卡马克磁约束装置中等离子体边缘区域流与湍流涨落之间的唯象耦合机制。对于该二维系统，推导了相应的哈密顿-雅可比方程，并采用一种将物理信息神经网络与通过矢量场分解设计的损失函数相结合的机器学习方法进行数值求解。这产生了关于系统准势的信息，能够进一步计算耦合系统中罕见状态转换的最可能路径。与经典二维低到高约束转换模型相比，所提出的系统具有更易于实验测量的状态变量且有更全面的物理基础，还能自洽地描述托卡马克装置启动阶段的动力学行为。
英文摘要
This work presents a two-dimensional coupled Low-to-High confinement transition system based on the phenomenological coupling mechanism between zonal flows and turbulent fluctuations at the plasma edge in tokamak magnetic confinement devices. For this two-dimensional system, the corresponding Hamilton-Jacobi equation is derived, and a machine learning approach combining physics-informed neural networks with a loss function designed via vector field decomposition is employed to numerically solve it. This yields information about the system's quasipotential, enabling further computation of the most probable path for the rare event of a state transition in the coupled system. Compared with classical two-dimensional Low-to-High confinement transition models, the proposed system features state variables that are more accessible to experimental measurement and has a more comprehensive physical foundation. Moreover, it self-consistently describes the dynamical behavior of tokamak devices during the startup phase.
