Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths

Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and dynamics, through summing over a huge manifold of all possible paths. From computational simulational perspectives, ergodic tracking whole is hard problem. Machine learning can help, in efficient manner, to identify relevant subspace intrinsic structure residing at small fraction vast manifold. In this work, we propose generator mechanical systems, which efficiently generates paths with fixed endpoints, from (low-dimensional) latent space by targeting desired density Euclidean space-time. With such generators, as well ground-state wave function be estimated generic potential energy. Our work provides alternative approach calculating function, paves way toward generative modeling paths, offers different perspective understand quantum-classical correspondence deep learning.