Fourier-flow model generating Feynman paths

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 physical observables' estimation translates into weighted sum over all possible paths. The underlying difficulty is tackle whole manifold from finite samples that can effectively represent propagator dictated probability distribution. Modern generative models in machine learning handle representing distribution with high computational efficiency. In this study, we propose Fourier-flow model simulate generate paths systems. demonstration, validate generator on harmonic anharmonic oscillators. latter double-well system without analytic solutions. To preserve periodic condition system, Fourier transformation introduced flow approach Matsubara representation. With novel development, ground-state wave function low-lying energy levels are estimated accurately. Our method offers new avenue investigate systems assisted integral solving.