Deep Learning Beyond Lefschetz Thimbles

Abstract

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally-expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea is to obtain a few field configurations via the flow equations to train a feed-forward neural network. The trained network defines a new manifold of integration which reduces the sign problem and can be rapidly sampled. We present results for the $1+1$ dimensional Thirring model with Wilson fermions on sizable lattices. In addition to the gain in speed, the parameterization of the integration manifold we use avoids the "trapping" of Monte Carlo chains which plagues large-flow calculations, a considerable shortcoming of the previous attempts.

12 pages, 4 figures

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Cited by in corpus (44)

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• Application of neural network to sign problem via path optimization method
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Finite Density $QE{D}_{1+1}$ Near Lefschetz Thimbles
• Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop
• Path integral contour deformations for observables in $SU(N)$ gauge theory
• Path integral contour deformations for noisy observables
• Normalizing Flows and the Real-Time Sign Problem
• Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems
• Machine Learning Estimators for Lattice QCD Observables
• A complex path around the sign problem
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Lattice Scalar Field Theory At Complex Coupling
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Taylor expansions on Lefschetz thimbles (and not only that)
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
• Continuous-mixture Autoregressive Networks for efficient variational calculation of many-body systems
• Benchmark results in the 2D lattice Thirring model with a chemical potential
• Modifying partition functions: a way to solve the sign problem
• Path optimization for $U(1)$ gauge theory with complexified parameters
• Simulating Yang-Mills theories with a complex coupling
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• The Ising Model with Hybrid Monte Carlo
• Semidefinite Programs at Finite Fermion Density
• Settling an old story: solution of the Thirring model in thimble regularization
• Deep Learning of Fermion Sign Fluctuations
• Optimisation of complex integration contours at higher order
• Convex optimization and contour deformations
• Anatomy of a strong residual sign problem on the thimbles
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Sign optimization and complex saddle points in one-dimensional QCD
• Real-time quantum dynamics, path integrals and the method of thimbles
• Neural Network Statistical Mechanics
• A saddle-point finder and its application to the spin foam model
• Is it worth the effort to find Lefschetz thimbles? Integration contours with numerically optimal signal-to-noise ratios in simple fermionic toy models
• Path optimization method for the sign problem caused by fermion determinant
• Complex path simulations of geometrically frustrated ladders
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo