Efficient and Scalable Approach to Equilibrium Conditional Simulation of Gibbs Markov Random Fields

TL;DR

This paper presents an automated hybrid Monte Carlo method for efficient and scalable equilibrium simulation of a Gibbs Markov random field, significantly improving performance in low-temperature, sparse data scenarios.

Contribution

The paper introduces a hybrid Monte Carlo approach that enhances the efficiency of equilibrium simulation for a modified planar rotator Gibbs MRF, especially under challenging conditions.

Findings

HMC outperforms standard Metropolis in computational efficiency.

HMC achieves faster convergence to equilibrium at low temperatures.

Improved prediction accuracy in gap filling tasks.

Abstract

We study the performance of an automated hybrid Monte Carlo (HMC) approach for conditional simulation of a recently proposed, single-parameter Gibbs Markov random field (Gibbs MRF). The MRF is based on a modified version of the planar rotator (MPR) model and is used for efficient gap filling in gridded data. HMC combines the deterministic over-relaxation method and the stochastic Metropolis update with dynamically adjusted restriction and performs automatic detection of the crossover to the targeted equilibrium state. We focus on the ability of the algorithm to efficiently drive the system to equilibrium at very low temperatures even with sparse conditioning data. These conditions are the most challenging computationally, requiring extremely long relaxation times if simulated by means of the standard Metropolis algorithm. We demonstrate that HMC has considerable benefits in terms of both computational efficiency and prediction performance of the MPR method.