Supervised learning in φ^4 lattice field theory

Abstract

Lattice quantum field theory is a frequently used approach to explore, describe and investigate physical phenomena computationally using numerical simulations. Machine Learning (ML) has the potential to provide useful tools and techniques which may assist in this context. For this purpose ML algorithms have to respect certain symmetries which are essential for applications in physics. In this work we focus on constructing translationally invariant Convolutional Neural Networks (CNNs) and explore their application to a dualized description of the discretized Klein-Gordon phi^4 scalar field theory. Another advantage of the architectures we explore, besides translational invariance, is the possibility to provide differently sized inputs to the CNN. We perform a regression and classification task to evaluate whether these ML algorithms are able to predict physical observables.The models were able to perform accurate predictions for field configurations with a lattice size on which they were trained. More interestingly, they were able to generalize to larger lattice sizes and deliver comparable predictions.