A Generative-Model approach to path integrals

Abstract

The Feynman path integral formalism is one of the most elegant approaches to Quantum Mechanics, and it provides an alternative and more intuitive manner of understanding the relation between quantum and classical mechanics. Nevertheless, path integrals have the drawback of being utterly difficult to compute, which is why computational methods tackling this issue are in order. In this work we explore the possibilities that Machine Learning has to offer in such computational scenarios. Inspired by the standard Markov-Chain Monte Carlo approach to path integrals, we design a generative neural network that can infer the path distribution from previously generated paths and can also generate new paths equally distributed. Our method has the fundamental advantage over the Markov Chain technique that, once trained, it can sample random paths efficiently and in parallel. The ML model that we employ is not specifically tailored to solve path integrals, and in fact it can be readily embedded in any setting where learning or sampling from a probability density function is needed.