Hamiltonian Monte Carlo reconstruction from peculiar velocities

TL;DR

This paper introduces Hamlet, a Hamiltonian Monte Carlo-based algorithm for efficiently reconstructing large-scale cosmic density and velocity fields from peculiar velocity surveys, significantly outperforming previous methods in speed.

Contribution

The paper presents Hamlet, a novel HMC-based reconstruction method that is faster and more efficient than prior Gibbs sampling approaches, enabling analysis of larger datasets.

Findings

Hamlet outperforms previous methods by 2-4 orders of magnitude in CPU time.

The algorithm effectively reconstructs large-scale structures from mock cosmic flow data.

Parallel GPU implementation enhances computational efficiency.

Abstract

The problem of the reconstruction of the large scale density and velocity fields from peculiar velocities surveys is addressed here within a Bayesian framework by means of Hamiltonian Monte Carlo (HMC) sampling. The HAmiltonian Monte carlo reconstruction of the Local EnvironmenT (Hamlet) algorithm is designed to reconstruct the linear large scale density and velocity fields in conjunction with the undoing of lognormal bias in the derived distances and velocities of peculiar velocities surveys such as the Cosmicflows data. The Hamlet code has been tested against Cosmicflows mock catalogs consisting of up to 30 000 data points with mock errors akin to those of the Cosmicflows-3 data, within the framework of the LCDM standard model of cosmology. The Hamlet code outperforms previous applications of Gibbs sampling MCMC reconstruction from the Cosmicflows-3 data by two to four orders of magnitude in CPU time. The gain in performance is due to the inherent higher efficiency of the HMC algorithm and due to parallel computing on GPUs rather than CPUs. This gain will enable an increase in the reconstruction of the large scale structure from the upcoming Cosmicfows-4 data and the setting of constrained initial conditions for cosmological high resolution simulations.