Counting Lattice Points in the Sphere using Deep Neural Networks

This paper presents a deep learning model for regression to predict the number of lattice points inside the n-dimensional hypersphere. The number of points depends primarily on the lattice generator matrix and the sphere radius, which are used as inputs for the proposed deep neural network (DNN). To see the accuracy of the DNN model, we use some known lattices. Obtained results are compared to mathematical existing bounds in the literature. Our numerical results reveal that our model gives an accurate prediction, of around 80% percent, on the number of lattice points in the sphere.