Fourier-Flow model generating Feynman paths

Abstract

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.

References in corpus (24)

• Quantum Monte Carlo methods for nuclear physics
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Event Generation with Normalizing Flows
• Equivariant flow-based sampling for lattice gauge theory
• Neural Network Renormalization Group
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Sampling using $SU(N)$ gauge equivariant flows
• i-flow: High-dimensional Integration and Sampling with Normalizing Flows
• Regressive and generative neural networks for scalar field theory
• Identifying the nature of the QCD transition in relativistic collision of heavy nuclei with deep learning
• Lattice gauge equivariant convolutional neural networks
• A machine learning study to identify spinodal clumping in high energy nuclear collisions
• Machine Learning Holographic Mapping by Neural Network Renormalization Group
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Deep learning stochastic processes with QCD phase transition
• Stochastic normalizing flows as non-equilibrium transformations
• A fast centrality-meter for heavy-ion collisions at the CBM experiment
• Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks
• Continuous-mixture Autoregressive Networks for efficient variational calculation of many-body systems
• Quasi-Monte Carlo methods for lattice systems: a first look
• Dyonic black hole degeneracies in $\mathcal{N}=4$ string theory from Dabholkar-Harvey degeneracies
• User's guide to Monte Carlo methods for evaluating path integrals
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Gauge invariant input to neural network for path optimization method

Cited by in corpus (9)

• Phase Transition Study meets Machine Learning
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
• Solving Schrodinger equations using physically constrained neural network
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Building imaginary-time thermal field theory with artificial neural networks
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• The neural networks with tensor weights and emergent fermionic Wick rules in the large-width limit
• A comparative lattice analysis of $SU(2)$ dark gluebal