Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State
激发Pfaffians:跨结构和状态的广义神经波函数
Nicholas Gao, Till Grutschus, Frank Noé, Stephan Günnemann
AI总结 提出多态重要性采样(MSIS)和激发Pfaffians架构,以近恒定样本量高效计算多态重叠,并在单个神经网络中表示多个激发态,实现更快训练和更多状态建模。
详情
变分蒙特卡洛(VMC)中的神经网络波函数在精确表示基态和激发态方面取得了巨大成功。然而,在状态重叠中实现足够的数值精度需要增加蒙特卡洛样本数量,从而增加计算成本,且随状态数增加。我们提出了一种近乎恒定样本量的方法——多态重要性采样(MSIS),利用来自所有状态的样本来估计成对重叠。为了高效评估所有样本的所有状态,我们引入了激发Pfaffians。受Hartree-Fock启发,该架构在单个神经网络内表示多个状态。激发Pfaffians还作为广义波函数,允许单个模型表示多态势能面。在碳二聚体上,我们匹配了$O(N_s^4)$标度的自然激发态,同时训练速度提高了$>200$倍,并建模了多50%的状态。我们有利的标度使我们能够首次使用神经网络找到铍原子的所有不同能级。最后,我们证明了单个波函数可以表示不同分子中的激发态。
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.