  As an alternative but unified and more fundamental description for quantum
physics, Feynman path integrals generalize the classical action principle to a
probabilistic perspective, under which the physical observables' estimation
translates into a weighted sum over all possible paths. The underlying
difficulty is to tackle the whole path manifold from finite samples that can
effectively represent the Feynman propagator dictated probability distribution.
Modern generative models in machine learning can handle learning and
representing probability distribution with high computational efficiency. In
this study, we propose a Fourier-flow generative model to simulate the Feynman
propagator and generate paths for quantum systems. As demonstration, we
validate the path generator on the harmonic and anharmonic oscillators. The
latter is a double-well system without analytic solutions. To preserve the
periodic condition for the system, the Fourier transformation is introduced
into the flow model to approach a Matsubara representation. With this novel
development, the ground-state wave function and low-lying energy levels are
estimated accurately. Our method offers a new avenue to investigate quantum
systems with machine learning assisted Feynman Path integral solving.
