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We study the performance of an automated hybrid Monte Carlo (HMC) approachfor conditional simulation of a recently proposed, single-parameter GibbsMarkov random field (Gibbs MRF). The MRF is based on a modified version of theplanar rotator (MPR) model and is used for efficient gap filling in griddeddata. HMC combines the deterministic over-relaxation method and the stochasticMetropolis update with dynamically adjusted restriction and performs automaticdetection of the crossover to the targeted equilibrium state. We focus on theability of the algorithm to efficiently drive the system to equilibrium at verylow temperatures even with sparse conditioning data. These conditions are themost challenging computationally, requiring extremely long relaxation times ifsimulated by means of the standard Metropolis algorithm. We demonstrate thatHMC has considerable benefits in terms of both computational efficiency andprediction performance of the MPR method.

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