发表机构
Nanjing University; University of Massachusetts; Collaborative Innovation Center of Advanced Microstructures, Nanjing University; Jiangsu Physical Science Research Center; Hefei National Laboratory; A. Alikhanyan National Science Laboratory（南京大学; 马萨诸塞大学; 南京大学人工微结构科学与技术协同创新中心; 江苏物理科学研究中心; 合肥国家实验室; A.阿利哈尼亚国家科学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出无偏直接梯度估计器和自适应最小方差相位估计器，通过提高弱梯度信噪比克服神经网络变分优化的训练障碍，实现更高效、更精确的量子多体与化学计算。
AI 中文摘要
神经网络为科学计算提供了表达力强的表示。然而，即使表达力足够的网络也可能在弱梯度区域遭遇训练失败，限制了它们在量子多体物理和从头算量子化学中的实际应用。在此，我们推导了一个无偏的直接梯度估计器，并引入了用于神经网络变分优化的自适应最小方差相位（AMVP）估计器。通过提高弱梯度的信噪比，这些方法使得在先前训练失败的场景中能够进行可靠的科学计算，同时大幅降低计算成本。该框架使紧凑网络能够在相关通量模型上以超过一个数量级的更少GPU时间胜过更大且经过精细调优的默认标准估计器模型，并最终超过密度矩阵重整化群（DMRG）的精度。它还在N$_2$键断裂中实现了化学精度，并首次在具有显式自旋轨道耦合的重元素I$_2$中实现了化学精度。这些结果表明，梯度估计器的设计扩展了神经网络变分方法在精确科学计算中的能力。
英文摘要
Neural networks provide expressive representations for scientific computing. However, even sufficiently expressive networks can suffer training failure in weak-gradient regimes, limiting their practical use in quantum many-body physics and ab initio quantum chemistry. Here we derive an unbiased direct gradient estimator and introduce the adaptive minimum-variance phase (AMVP) estimator for neural-network variational optimization. By improving the signal-to-noise ratio of weak gradients, these methods enable reliable scientific calculations where training previously failed, while substantially reducing computational cost. The framework enables compact networks to outperform larger and fine-tuned default standard-estimator models with over an order of magnitude less GPU time on correlated flux models, and ultimately exceed the density matrix renormalization group (DMRG) accuracy. It further achieves chemical accuracy in N$_2$ bond breaking and, for the first time, in heavy-element I$_2$ with explicit spin-orbit coupling. These results demonstrate that gradient-estimator design expands the capabilities of neural-network variational methods for accurate scientific computing.
Comments10 pages, 4 figures; partially supersedes arXiv:2606.13912
