论文标题
第一原理物理信息的神经网络，用于量子波形和特征值表面
First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces
论文作者
论文摘要
物理信息的神经网络已被广泛应用于学习微分方程的一般参数解决方案。在这里，我们提出了一个神经网络，以发现量子系统的参数特征值和特征功能表面。我们应用我们的方法来求解氢分子离子。这是一种Ab-Initio深度学习方法，它可以用库仑电势求解Schrodinger方程，从而产生逼真的波形，其中包括在离子位置上的尖尖。神经溶液是原子间距离的连续且可区分的功能，其衍生物是通过应用自动分化来分析计算的。解决方案的这种参数和分析形式对于进一步的计算（例如测定力场）很有用。
Physics-informed neural networks have been widely applied to learn general parametric solutions of differential equations. Here, we propose a neural network to discover parametric eigenvalue and eigenfunction surfaces of quantum systems. We apply our method to solve the hydrogen molecular ion. This is an ab-initio deep learning method that solves the Schrodinger equation with the Coulomb potential yielding realistic wavefunctions that include a cusp at the ion positions. The neural solutions are continuous and differentiable functions of the interatomic distance and their derivatives are analytically calculated by applying automatic differentiation. Such a parametric and analytical form of the solutions is useful for further calculations such as the determination of force fields.
