用统一模型高效计算多个量子态波函数，大幅提速并扩展应用范围。
Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State
- 设计多态重要性采样与激发泊松行列式，共享样本提升效率
- 碳二聚体计算速度超200倍，覆盖50%更多能级，符合O(N_s⁴)缩放规律
- 单个模型可表征多种分子的激发态，适合多态系统模拟
变分蒙特卡洛中的神经网络波函数在精确描述基态和激发态方面取得显著进展。然而，状态间重叠的数值精度随状态数量增加而需更多蒙特卡洛样本，导致计算成本上升。本文提出近似恒定采样量的多态重要性采样（MSIS）方法，利用所有状态的样本估计成对重叠。为高效评估所有状态的所有样本，引入激发泊松行列式（Excited Pfaffians）。受哈特里-福克启发，该架构将多个状态整合于单一神经网络中。激发泊松行列式亦作为广义波函数，使单个模型可表示多态势能面。在碳二聚体上，实现与$O(N_s^4)$缩放一致的激发态，并训练速度提升200倍以上，建模状态数增加50%。优异缩放性能使我们首次使用神经网络求解铍原子所有独立能级。最终，证明单个波函数可跨多种分子表征激发态。
原文摘要 · Abstract (English)
Neural-network wave functions in Variational Monte Carlo (VMC) have achieved great success in accurately representing both ground and excited states. However, achieving sufficient numerical accuracy in state overlaps requires increasing the number of Monte Carlo samples, and consequently the computational cost, with the number of states. We present a nearly constant sample-size approach, Multi-State Importance Sampling (MSIS), that leverages samples from all states to estimate pairwise overlap. To efficiently evaluate all states for all samples, we introduce Excited Pfaffians. Inspired by Hartree-Fock, this architecture represents many states within a single neural network. Excited Pfaffians also serve as generalized wave functions, allowing a single model to represent multi-state potential energy surfaces. On the carbon dimer, we match the $O(N_s^4)$-scaling natural excited states while training $>200\times$ faster and modeling 50% more states. Our favorable scaling enables us to be the first to use neural networks to find all distinct energy levels of the beryllium atom. Finally, we demonstrate that a single wave function can represent excited states across various molecules.
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