Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining Monte Carlo methods with unsupervised training of neural networks has recently been proposed as a promising approach to overcome the curse of dimensionality in this setting and to obtain accurate wavefunctions for individual molecules at a moderately scaling computational cost. These methods currently do not exploit the regularity exhibited by wavefunctions with respect to their molecular geometries. Inspired by recent successful applications of deep transfer learning in machine translation and computer vision tasks, we attempt to leverage this regularity by introducing a weight-sharing constraint when optimizing neural network-based models for different molecular geometries. That is, we restrict the optimization process such that up to 95 percent of weights in a neural network model are in fact equal across varying molecular geometries. We find that this technique can accelerate optimization when considering sets of nuclear geometries of the same molecule by an order of magnitude and that it opens a promising route towards pre-trained neural network wavefunctions that yield high accuracy even across different molecules.

本文介绍了一种通过引入神经网络和Monte Carlo方法相结合，结合深度迁移学习的方法来解决当前高精度计算方法在计算与电子相互作用的粒子数量较大时的计算成本大，探索引入权重共享约束的优化过程，使神经网络模型的95%的权重可以在变化的分子几何图案之间使用，从而加速优化。实现这一技术可以加速相同分子的核几何集的优化一倍，开辟了一条有希望的路线，可以产生预先训练的神经网络波函数，即使在不同的分子上也可以产生高精度。

使用共享权重深度神经网络求解多核几何下的电子薛定谔方程