SAIL: A CUDA-based implementation of the simulated annealing for the inverse Laplace transform problem

TL;DR

This paper presents a CUDA-accelerated parallel implementation of the simulated annealing algorithm to solve the inverse Laplace transform problem, improving efficiency and convergence through local updates and imprinted branching.

Contribution

The authors introduce a CUDA-based parallel annealing algorithm with local updates and imprinted branching for more efficient inverse Laplace transform reconstruction.

Findings

Effective reconstruction of spectral functions demonstrated.

Parallel implementation accelerates the annealing process.

Error sensitivity analyzed in spectral reconstruction.

Abstract

We developed a CUDA-based parallelization of the annealing method for the inverse Laplace transform problem. The algorithm is based on annealing algorithm and minimizes residue of the reconstruction of the spectral function. We introduce local updates which preserve first two sum rules and allow an efficient parallel CUDA implementation. Annealing is performed with the Monte Carlo method on a population of Markov walkers. We propose imprinted branching method to improve further the convergence of the anneal. The algorithm is tested on truncated double-peak Lorentzian spectrum with examples of how the error in the input data affects the reconstruction.