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Feynman path integrals provide an elegant, classically inspiredrepresentation for the quantum propagator and the quantum dynamics, throughsumming over a huge manifold of all possible paths. From computational andsimulational perspectives, the ergodic tracking of the whole path manifold is ahard problem. Machine learning can help, in an efficient manner, to identifythe relevant subspace and the intrinsic structure residing at a small fractionof the vast path manifold. In this work, we propose the Feynman path generatorfor quantum mechanical systems, which efficiently generates Feynman paths withfixed endpoints, from a (low-dimensional) latent space and by targeting adesired density of paths in the Euclidean space-time. With such pathgenerators, the Euclidean propagator as well as the ground-state wave functioncan be estimated efficiently for a generic potential energy. Our work providesan alternative approach for calculating the quantum propagator and theground-state wave function, paves the way toward generative modeling of quantummechanical Feynman paths, and offers a different perspective to understand thequantum-classical correspondence through deep learning.

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