保概率Transformer用于含时薛定谔方程
Probability-Preserving Transformer for the Time-Dependent Schrödinger Equation
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- University of Education Lahore（拉合尔教育大学）
- Xiamen University（厦门大学）
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中文总结 AI 辅助
该研究针对含时薛定谔方程求解，提出将概率守恒作为硬约束的Transformer架构，相比传统软约束方法，兼具物理精确性与计算优势。
中文摘要 AI 辅助
传统数值方法求解含时薛定谔方程（TDSE）计算量极大，Transformer模型是颇具吸引力的替代方案，但标准实现依赖软约束，无法严格保证概率守恒。本文提出一种将TDSE概率守恒作为硬约束的Transformer架构，该设计在时间演化中固有保证幺正性，无需重复再训练。实证结果表明，这种硬约束方法不仅物理上精确，而且在计算上优于传统软约束方法。
英文摘要
Solving the time-dependent Schrödinger equation (TDSE) via traditional numerical methods is computationally intensive. Transformer models offer a compelling alternative, but standard implementations rely on soft constraints that cannot rigorously guarantee probability conservation. Here, we introduce a Transformer architecture that enforces TDSE probability conservation as a hard constraint. The design intrinsically ensures unitarity across temporal evolution without requiring repeated retraining. Our empirical findings show that this hard-constraint approach is not only physically exact but also computationally superior to conventional soft-constraint methods.
