Learned Optimizers for Analytic Continuation

TL;DR

This paper introduces a neural network-based optimizer for analytic continuation that replaces ill-posed inverse problems with well-conditioned surrogates, achieving high-quality solutions efficiently and with better parameter use.

Contribution

It presents a novel neural network approach using convex optimization to improve analytic continuation, outperforming traditional methods in speed and quality.

Findings

High-quality solutions with low time cost

Better parameter efficiency than heuristic networks

Enhanced maximum entropy performance

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.