标题： 使用神经常微分方程优化托卡马克中受控燃烧等离子体的外部源 显示英文标题

标题： Optimizing External Sources for Controlled Burning Plasma in Tokamaks with Neural Ordinary Differential Equations

摘要： 在托卡马克中实现受控燃烧等离子体需要精确调节外部粒子和能量源，以达到并维持目标核心密度和温度。 本工作提出了一种逆向建模方法，使用基于神经微分方程（Neural ODEs）的多节点等离子体动力学模型。 给定节点量（如氘密度或电子温度）的时间演化，我们计算外部源分布（如中性束注入（NBI）功率），这些分布驱动等离子体朝向指定行为发展。 该方法在NeuralPlasmaODE框架内实现，该框架模拟多区域、多时间尺度的输运，并包含包括辐射、辅助加热和节点间能量交换在内的物理机制。 通过将控制任务表述为优化问题，我们使用通过Neural ODE求解器的自动微分来最小化模拟轨迹与目标轨迹之间的差异。 此框架将正向仿真工具转化为控制导向模型，并为当前和未来聚变装置计算外部源分布提供了一种实用方法。 显示英文摘要

摘要： Achieving controlled burning plasma in tokamaks requires precise regulation of external particle and energy sources to reach and maintain target core densities and temperatures. This work presents an inverse modeling approach using a multinodal plasma dynamics model based on neural ordinary differential equations (Neural ODEs). Given a desired time evolution of nodal quantities such as deuteron density or electron temperature, we compute the external source profiles, such as neutral beam injection (NBI) power, that drive the plasma toward the specified behavior. The approach is implemented within the NeuralPlasmaODE framework, which models multi-region, multi-timescale transport and incorporates physical mechanisms including radiation, auxiliary heating, and internodal energy exchange. By formulating the control task as an optimization problem, we use automatic differentiation through the Neural ODE solver to minimize the discrepancy between simulated and target trajectories. This framework transforms the forward simulation tool into a control-oriented model and provides a practical method for computing external source profiles in both current and future fusion devices.