发表机构
Great Bay University; Jinan University; Great Bay Institute for Advanced Study（大湾区大学; 暨南大学; 大湾区高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出物理约束神经流图，直接在单位球面学习自旋动力学有限时间映射，优于适配LSTM，实现低范数漂移的长时程物理可容许预测，缓解传统细步长积分的计算瓶颈。
AI 中文摘要
传统的电流驱动磁化模拟依赖于自旋转移矩朗道-利夫希茨-吉尔伯特方程的细步长积分，这在参数扫描和控制搜索中造成了计算瓶颈。本研究提出一种物理约束神经流图，直接在单位球面上学习有限时间动力学。该模型将当前磁化强度、自旋矩强度和请求的时间跨度映射为未来状态，仅需一次前向传播。切空间投影和球面回缩在递归、 composition-consistent（组合一致性）展开过程中保持单位磁化强度。我们在域内矩作用下的单自旋轨迹以及先前未见过的更强驱动上验证该框架。在训练时间范围之外，其域内均方根误差为$0.00425$，范数漂移处于$10^{-7}$量级。该流图在域内精度和几何稳定性上优于适配后的长短期记忆网络（LSTM），尽管LSTM保留略低的分布外状态误差。所得的几何保持传播子减少了对细步长积分的依赖，实现了物理上可容许的长时程预测。
英文摘要
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.
