Learned Optimizers for Analytic Continuation

Abstract

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex optimization and replace the ill-posed inverse problem by a sequence of well-conditioned surrogate problems. After training, the learned optimizers are able to give a solution of high quality with low time cost and achieve higher parameter efficiency than heuristic fully-connected networks. The output can also be used as a neural default model to improve the maximum entropy for better performance. Our methods may be easily extended to other high-dimensional inverse problems via large-scale pretraining.

arXiv comment11 pages, 7 figures, 6 tables

References in corpus (27)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Boltzmann Machine
• Learning a local Hamiltonian from local measurements
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
• Nevanlinna Analytical Continuation
• Constrained sampling method for analytic continuation
• Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
• Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data
• Artificial Neural Network Approach to the Analytic Continuation Problem
• Incipient antiferromagnetism and low-energy excitations in the half-filled two-dimensional Hubbard model
• Analytic continuation via domain-knowledge free machine learning
• Analytical continuation of imaginary axis data for optical conductivity
• Why Gabor Frames? Two Fundamental Measures of Coherence and Their Role in Model Selection
• Sparse Modeling in Quantum Many-Body Problems
• Analytical continuation of imaginary axis data using maximum entropy
• Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
• Maximum Entropy Analytic Continuation for Spectral Functions with Non-Positive Spectral Weight
• The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
• Maximum Quantum Entropy Method
• Extending the average spectrum method: Grid points sampling and density averaging
• SpM: Sparse modeling tool for analytic continuation of imaginary-time Green's function
• Hybridization fluctuations in the half-filled periodic Anderson model
• Bayesian parametric analytic continuation of Green's functions
• Analytic continuation with Padé decomposition
• Effective classical correspondence of the Mott transition

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