🤖 AI Summary
该研究通过设计梯度估计器解决了神经网络在弱梯度区域的训练失败问题，提高了科学计算中的准确性和效率。
📝 Abstract
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.