Gibbs Markov random fields with continuous values based on the modified planar rotator model

Žukovič, M.; Hristopulos, Dionissios T.

doi:10.1103/physreve.98.062135

Cited by 13 publications

(14 citation statements)

References 63 publications

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“…The temperature is the only simulation parameter and needs to be inferred from the incomplete data. Then, a conditional Monte Carlo simulation, in which only the spins at the prediction locations are allowed to change their states, is performed using the so-called hybrid algorithm [5]. By averaging over multiple configurations in equilibrium, one can obtain predictions on the discretized two-dimensional missing data.…”

Section: Model and Methodsmentioning

confidence: 99%

Numerical Precision Effects on GPU Simulation of Massive Spatial Data, Based on the Modified Planar Rotator Model

2020

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The present research builds on a recently proposed spatial prediction method for discretized two-dimensional data, based on a suitably modified planar rotator (MPR) spin model from statistical physics. This approach maps the measured data onto interacting spins and, exploiting spatial correlations between them, which are similar to those present in geostatistical data, predicts the data at unmeasured locations. Due to the shortrange nature of the spin pair interactions in the MPR model, parallel implementation of the prediction algorithm on graphical processing units (GPUs) is a natural way of increasing its efficiency. In this work we study the effects of reduced computing precision as well as GPU-based hardware intrinsic functions on the speedup and accuracy of the MPR-based prediction and explore which aspects of the simulation can potentially benefit the most from the reduced precision. It is found that, particularly for massive data sets, a thoughtful precision setting of the GPU implementation can significantly increase the computational efficiency, while incurring little to no degradation in the prediction accuracy.

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Section: Model and Methodsmentioning

confidence: 99%

Numerical Precision Effects on GPU Simulation of Massive Spatial Data, Based on the Modified Planar Rotator Model

2020

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“…at low temperatures, due to very low acceptance rate (proportional to exp(−∆E/T ), where ∆E = E new − E old is the energy difference between the new and old states). This leads to extremely long relaxation times in the low-T limit, which is the typical parameter region for the MPR prediction (T ≈ 10 −2 ) [7]. Efficient use of the MPR method requires an updating scheme that is able to drive the system to equilibrium fast, i.e., with the shortest possible relaxation time.…”

Section: Hybrid Monte Carlomentioning

confidence: 99%

“…Recently, we have introduced a novel Gibbs Markov random field for prediction of spatial data on regular grids, based on the modified planar rotator (MPR) model [7]. We also proposed an efficient and automated hybrid Monte Carlo (HMC) approach for the conditional simulation of the model.…”

Section: Introductionmentioning

confidence: 99%

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

Žukovič

Hristopulos

2020

EPJ Web Conf.

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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.

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“…Nevertheless, there have been some attempts to apply several of these models, such as the binary Ising, q-state Potts and clock, and continuous planar rotator models, to image restoration [24][25][26][27][28][29] and geostatistical [30][31][32][33] problems.…”

Section: Introductionmentioning

confidence: 99%

Spatial data modeling by means of Gibbs Markov random fields based on a generalized planar rotator model

Žukovič¹,

Hristopulos²

2022

Preprint

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We introduce a Gibbs Markov random field for spatial data on Cartesian grids which is based on the generalized planar rotator (GPR) model. The GPR model generalizes the recently proposed modified planar rotator (MPR) model by including in the Hamiltonian additional terms that better capture realistic features of spatial data, such as smoothness, non-Gaussianity, and geometric anisotropy. In particular, the GPR model includes up to infinite number of higher-order harmonics with exponentially vanishing interaction strength, directional dependence of the bilinear interaction term between nearest grid neighbors, longer-distance neighbor interactions, and two types of an external bias field. Hence, in contrast with the single-parameter MPR model, the GPR model features five additional parameters: the number n of higher-order terms and the parameter α controlling their decay rate, the exchange anisotropy parameter J nn , the further-neighbor interaction coupling J fn , and the external field (bias) parameters K (or K ′ ). We present numerical tests on various synthetic data which demonstrate the effects of the respective terms on the model's prediction performance and we discuss these results in connection with the data properties.

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Gibbs Markov random fields with continuous values based on the modified planar rotator model

Cited by 13 publications

References 63 publications

Numerical Precision Effects on GPU Simulation of Massive Spatial Data, Based on the Modified Planar Rotator Model

Numerical Precision Effects on GPU Simulation of Massive Spatial Data, Based on the Modified Planar Rotator Model

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

Spatial data modeling by means of Gibbs Markov random fields based on a generalized planar rotator model

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