将神经网络量子态扩展用于从头量子化学计算
Scaling Neural Network Quantum States for Ab Initio Quantum Chemistry
- State Key Lab of Brain-Machine Intelligence, Zhejiang University（浙江大学脑机智能全国重点实验室）
- College of Artificial Intelligence, Zhejiang University（浙江大学人工智能学院）
- State Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China（中国科学技术大学精密与智能化学全国重点实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对物理条件自回归神经网络量子态，探究模型规模与优化步数对从头量子化学计算精度的影响，提出相互作用标度律，为计算预算内选择模型与优化步数提供决策规则，且该标度趋势在N₂微调中持续。
AI中文摘要：
神经网络量子态（NNQSs）可表示多电子波函数，无需显式枚举行列式空间，但其精度同时取决于模型规模和变分优化的工作量。本文针对一种物理条件自回归NNQS开展研究，该模型分别在两个包含六个分子的源基准数据集上训练。在八种模型规模和五个优化里程碑中，我们发现模型规模与优化步数共同决定能量误差；更大模型的容量优势在优化充分时更为显著，而额外优化的收益随模型规模变化。我们通过相互作用标度律刻画该耦合关系，并量化每个评估配置的累计计算量；得到的误差-计算量帕累托前沿为，在给定计算预算和评估范围内，联合选择模型规模与优化步数提供实用决策规则。此外，我们发现该有益标度趋势在保留的N₂微调过程中持续存在，预训练模型的误差随模型规模增大而降低，且在Hard基准上预训练后误差下降更显著。综上，这些结果将自回归神经量子态纳入更广泛的经验神经标度框架，为从头量子化学的神经量子求解器系统扩展开辟了定量途径。
英文摘要：
Neural-network quantum states (NNQSs) can represent many-electron wave functions without explicitly enumerating the determinant space, but their accuracy depends jointly on model size and variational-optimization effort. Here we characterize this dependence for a physics-conditioned autoregressive NNQS trained separately on two six-molecule source benchmarks. Across eight model sizes and five optimization milestones, we find that model size and optimization steps jointly shape the energy error. The capacity advantage of larger models becomes more apparent with sufficient optimization, while the returns from additional optimization vary with model size. We capture this coupling using an interaction scaling law and quantify the cumulative compute of each evaluated configuration. The resulting error-compute Pareto frontiers provide a practical decision rule for jointly selecting model size and optimization steps under a given compute budget within the evaluated range. Furthermore, we find that this beneficial scaling trend persists during fine-tuning on held-out N$_2$. Pretrained models show decreasing error with increasing model size, with a steeper reduction following pretraining on the Hard benchmark. Together, these results place autoregressive neural quantum states within the broader landscape of empirical neural scaling and open a quantitative route toward the systematic scaling of neural quantum solvers for ab initio quantum chemistry.
