A Hybrid Convolutional Neural Network and Grid Extrapolation Approach for Predicting Solutions of the Electronic Schrödinger Equation

Solving the many‐electron Schrödinger equation is central to numerous branches of physics, yet its computational complexity often poses challenges. In this work, we explore the integration of deep learning techniques to predict electronic properties for model systems, focusing on two distinct cases: (1) single‐electron properties from three‐dimensional (3D) potential representations, and (2) two‐electron properties of the hydrogen molecule () in six‐dimensional (6D) space. Our 3D model utilizes a deep convolutional neural network architecture to handle cubic potential inputs, while our 6D extension employs a modified architecture for the system. We augment our datasets with random rotations to address rotational invariance. Through comprehensive experiments, we demonstrate the effectiveness of our approach across dimensionalities. For the 6D case, we achieve high accuracy by using the network to predict grid‐dependent energies, which are then refined with a polynomial extrapolation scheme. This hybrid approach highlights deep learning's potential as a powerful accelerator for traditional grid‐based numerical methods in electronic structure calculations.