arXiv:2603.14515v2 Announce Type: replace 
Abstract: 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.

تم تحسين وظائف الموجة القائمة على الشبكات العصبية من خلال إدخال تقنية أخذ العينات متعددة الحالات (MSIS) وPfaffians المثارة، مما يسمح بتمثيل فعال لعدة حالات داخل شبكة عصبية واحدة. تقلل هذه الطريقة بشكل كبير من تكاليف الحوسبة مع الحفاظ على الدقة في تقدير تداخل الحالات، كما تم إثباته على ديمر الكربون.

Las funciones de onda basadas en redes neuronales han sido mejoradas mediante la introducción del muestreo de importancia de múltiples estados (MSIS) y los Pfaffianos excitados, que permiten una representación eficiente de múltiples estados dentro de una sola red neuronal. Este enfoque reduce significativamente los costos computacionales mientras mantiene la precisión en la estimación de superposiciones de estados, demostrado especialmente en el dimero de carbono.

Les fonctions d'onde basées sur des réseaux de neurones ont été améliorées grâce à l'introduction de l'échantillonnage d'importance multi-états (MSIS) et des Pfaffiens excités, qui permettent une représentation efficace de plusieurs états au sein d'un seul réseau de neurones. Cette approche réduit considérablement les coûts de calcul tout en maintenant la précision dans l'estimation des chevauchements d'états, comme l'a démontré le cas du dimère de carbone.

Neural-network wave functions have been enhanced through the introduction of Multi-State Importance Sampling (MSIS) and Excited Pfaffians, which allow for efficient representation of multiple states within a single neural network. This approach significantly reduces computational costs while maintaining accuracy in estimating state overlaps, particularly demonstrated on the carbon dimer.