Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network

Abstract

This paper aims to present an approach to address the atom rearrangement problem by developing Convolutional Neural Network (CNN) models. These models predict the coordinates for atom movements while ensuring collision-free transitions and filling all vacancies in the target array. The process begins with designing a cost function for the assignment problem that incorporates constraints to prevent collisions and guarantee vacancy filling. We then build and train CNN models using datasets for three different grid sizes: 10×10, 13×13, and 21×21. Our models achieve high accuracy in predicting atom positions, with individual position accuracies of 99.63%, 98.93%, and 97.24%, respectively, for the aforementioned grid sizes. Despite limitations in training larger models due to hardware constraints, our approach demonstrates significant improvements in speed and accuracy. The final section of the paper presents detailed accuracy results and calculation times for each model, highlighting the potential of CNN-based methods in optimizing atom rearrangement processes.