Can machine learning efficiently predict symmetry breaking in physical problems like Bose-Einstein condensates?

Abstract

In this work, our objective is to evaluate whether machine learning algorithms combined with computational methods used in physical problems such as spontaneous symmetry breaking in Bose-Einstein condensates are capable of efficiently predicting results obtained from solutions of nonlinear equations. Thus, we use K-means algorithms, support vector machines (SVM) and artificial neural network (ANN) multilayer perceptron to evaluate the efficiency of each algorithm in the process of predicting theoretical results in regions where computational calculations cannot be performed. either by numerical inaccuracy or computational cost. The results show that sophisticated machine learning algorithms can predict the behavior of represented physical systems with a satisfactory quality, where we especially highlight the correct interpretation of the physical problem in border regions and/or transitions.