Modeling \(^4\)He\({_N}\) Clusters with Wave Functions Based on Neural Networks

A recently introduced neural network-based trial wave function, in combination with the variational Monte Carlo method, is applied to clusters of helium atoms of several sizes. Energies of clusters ranging from 11 to 24 atoms and radial distribution functions are reported in excellent agreement with those of the droplet model obtained with diffusion Monte Carlo. The abilities of neural networks to recognize patterns and relationships from distinct input features are explored, including identifying radial symmetry without explicitly considering it in the network inputs. The relation between data representation and the learning process is investigated, showing that high-quality data representations are critical for the efficient use of neural networks.