Deciphering the Small-Angle Scattering of Polydisperse Hard Spheres using Deep Learning

Abstract

We introduce a deep learning approach for analyzing the scattering function of the polydisperse hard spheres system. We use a variational autoencoder-based neural network to learn the bidirectional mapping between the scattering function and the system parameters including the volume fraction and polydispersity. Such that the trained model serves both as a generator that produce scattering function from the system parameters, and an inferrer that extract system parameters from the scattering function. We first generate a scattering dataset by carrying out molecular dynamics simulation of the polydisperse hard spheres modeled by the truncated-shifted Lennard-Jones model, then analyze the scattering function dataset using singular value decomposition to confirm the feasibility of dimensional compression. Then we split the dataset into training and testing set and train our neural network on the training set only. Our generator model produce scattering function with significant higher accuracy comparing to the traditional Percus-Yevick approximation and $β$ correction, and the inferrer model can extract the volume fraction and polydispersity with much higher accuracy than traditional model functions.