yancc：一种用于托卡马克和仿星器中经典输运的GPU加速可微求解器
yancc: A GPU-accelerated, differentiable solver for neoclassical transport in tokamaks and stellarators
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中文总结 AI 辅助
研究针对托卡马克和仿星器中经典输运问题，提出GPU加速可微求解器yancc。通过结合多种离散化方法求解漂移动力学方程，具有完全可微性。与其他代码基准测试显示其准确性高、速度快且内存占用低，适合用于仿星器相关优化等工作流程。
中文摘要 AI 辅助
我们展示了yancc，一种用于漂移动力学方程的新型GPU加速求解器，用于计算托卡马克和仿星器中的经典输运通量、流和电流。由于强平流主导、循环流、内部边界层、严重各向异性和高维性，漂移动力学方程在数值求解上具有挑战性。该代码可求解完整的四维漂移动力学方程（保留速度相关碰撞、能量散射和完整的种间耦合）以及简化的单能形式。离散化结合了速度上的麦克斯韦多项式配置网格与俯仰角和通量表面坐标上的有限差分，使用改进的迎风模板以提高多重网格效率的对角占优性。所得线性系统用多重网格预处理的 Krylov 方法求解。基于JAX构建的yancc是完全可微的，可实现基于梯度的优化和伴随灵敏度分析。与MONKES和SFINCS的基准测试表明，在一系列碰撞率、几何形状和多物种配置下，一致性在1%以内。yancc在每次扫描的基础上比SFINCS实现了大约一个数量级的加速，同时使用的内存减少了一个数量级，并且在整个碰撞率范围内运行时几乎保持不变。速度、低内存占用和可微性的结合使yancc非常适合集成到仿星器优化工作流程、不确定性量化和轮廓预测中。
英文摘要
We present yancc, a new GPU-accelerated solver for the drift kinetic equation that computes neoclassical transport fluxes, flows, and currents in tokamaks and stellarators. The drift kinetic equation is challenging to solve numerically due to strong advection-dominance, recirculating flows, internal boundary layers, severe anisotropy, and high dimensionality. The code solves both the full four-dimensional drift kinetic equation (retaining speed-dependent collisions, energy scattering, and full interspecies coupling), and the reduced monoenergetic form. The discretization combines a Maxwell polynomial collocation grid in speed with finite differences in pitch angle and the flux surface coordinates, using a modified upwind stencil designed to improve diagonal dominance for multigrid efficiency. The resulting linear system is solved with a multigrid-preconditioned Krylov method. Built in JAX, yancc is fully differentiable, enabling gradient-based optimization and adjoint sensitivity analysis. Benchmarks against MONKES and SFINCS show agreement within 1\% across a range of collisionalities, geometries, and multi-species configurations. yancc achieves roughly an order of magnitude speedup over SFINCS on a per-scan basis while using an order of magnitude less memory, with runtime remaining nearly flat across the full range of collisionality. The combination of speed, low memory footprint, and differentiability makes yancc well suited for integration into stellarator optimization workflows, uncertainty quantification, and profile prediction.
