用神经流映射实现自旋动力学长时预测，保持物理约束
Physics-Constrained Neural Flow Maps for Long-Horizon Prediction of Spin Dynamics
- 基于球面几何的神经流模型，单次前向传播预测未来状态
- 长时预测误差仅0.00425，磁化长度漂移低于10^-7
- 适合需要物理保真度的自旋电子学仿真与控制设计
传统电流驱动磁化模拟依赖自旋转移矩朗道-利夫希茨-吉尔伯特方程的细步积分，导致参数扫描和控制搜索计算瓶颈。本文提出一种物理约束的神经流映射，直接在单位球面上学习有限时间动力学。该模型将当前磁化、自旋扭矩强度及目标时间跨度映射为未来状态，通过切空间投影与球面回缩保证磁化长度恒定，并支持递归组合一致的滚动预测。在域内扭矩下的单自旋轨迹上验证，对未见过但更强的驱动力也具泛化能力。超出训练时域后，其域内均方根误差为0.00425，范数漂移维持在10^-7量级。相比改进的LSTM，该流模型在域内精度与几何稳定性上更优，尽管LSTM在分布外状态误差略低。所提几何保形传播器显著降低对细步积分的依赖，实现物理可接受的长时预测。
原文摘要 · Abstract (English)
Conventional simulation of current-driven magnetization relies on fine-step integration of the spin-transfer-torque Landau--Lifshitz--Gilbert equation, creating a computational bottleneck in parameter sweeps and control searches. In this work, we propose a physics-constrained neural flow map that learns finite-time dynamics directly on the unit sphere. The model maps the current magnetization, spin-torque strength, and requested time span to a future state in a single forward pass. Tangent-space projection and spherical retraction preserve unit magnetization during recursive, composition-consistent rollout. We validate the framework on single-spin trajectories under in-domain torques and previously unseen but stronger drive. Beyond the training horizon, it achieves an in-domain root mean square error of $0.00425$ with norm drift at the $10^{-7}$ level. The flow outperforms an adapted Long Short-Term Memory (LSTM) in in-domain accuracy and geometric stability, although the LSTM retains slightly lower out-of-distribution state error. The resulting geometry-preserving propagator reduces reliance on fine-step integration and enables physically admissible long-horizon prediction.
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