Deep-Learning-based Variational Monte Carlo (DL-VMC) has recently emerged as a highly accurate approach for finding approximate solutions to the many-electron Schr\"odinger equation. Despite its favorable scaling with the number of electrons, $\mathcal{O}(n_\text{el}^{4})$, the practical value of DL-VMC is limited by the high cost of optimizing the neural network weights for every system studied. To mitigate this problem, recent research has proposed optimizing a single neural network across multiple systems, reducing the cost per system. Here we extend this approach to solids, where similar but distinct calculations using different geometries, boundary conditions, and supercell sizes are often required. We show how to optimize a single ansatz across all of these variations, reducing the required number of optimization steps by an order of magnitude. Furthermore, we exploit the transfer capabilities of a pre-trained network. We successfully transfer a network, pre-trained on 2x2x2 supercells of LiH, to 3x3x3 supercells. This reduces the number of optimization steps required to simulate the large system by a factor of 50 compared to previous work.

翻译：基于深度学习的变分蒙特卡洛（DL-VMC）方法近期已成为求解多电子薛定谔方程近似解的高精度方法。尽管该方法随电子数具有$\mathcal{O}(n_\text{el}^{4})$的有利标度，但针对每个研究系统优化神经网络权重的高昂成本限制了DL-VMC的实际应用价值。为缓解这一问题，近期研究提出跨多个系统优化单一神经网络，从而降低单个系统的计算成本。本文将此方法推广至固体体系，此类研究常需对不同几何构型、边界条件及超胞尺寸进行相似但不同的计算。我们展示了如何跨越所有变量优化单一拟设，将所需优化步骤数量降低一个数量级。进一步地，我们利用预训练网络的迁移能力，成功将LiH 2×2×2超胞上预训练的网络迁移至3×3×3超胞，使大系统模拟所需的优化步骤数相比先前工作减少50倍。