Bayesian approach to the calculation of lateral interactions: NO/Rh(111)

Jansen, Apj Tonek; Popa, Cristina

doi:10.1103/physrevb.78.085404

Cited by 21 publications

(24 citation statements)

References 37 publications

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“…29 The total number of kinetic parameters ͑i.e., the adsorption energies and the pairwise, three and four particle interactions͒ to take into account in the kMC simulations is 13. Furthermore, only the short range pair interactions with the next-nearest and next-next-nearest neighbors seem to be important.…”

Section: Simulation and Discussionmentioning

confidence: 99%

Formation of ordered structures of NO on Rh(111)

2009

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In this work, several ͑unreported͒ structures of NO on Rh͑111͒ are presented for coverages ranging from 0-0.78 ML. The formation of these structures as evidenced experimentally by scanning tunneling microscopy ͑STM͒ images is explained using density-functional theory derived values for the lateral interactions and adsorption energies of NO on Rh͑111͒. Kinetic Monte Carlo simulations using the derived lateral interactions are performed to determine structures at finite temperatures. The resulting structures can be directly compared to the molecular arrangements observed in the STM experiment. The configuration of the first three structures that form for increasing coverage is the same both experimentally and theoretically. In all three structures, the molecules only occupy the fcc and hcp adsorption sites. Yet, at high coverage, at which the top adsorption sites become occupied, a discrepancy arises.

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Section: Simulation and Discussionmentioning

confidence: 99%

Formation of ordered structures of NO on Rh(111)

2009

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“…Furthermore, CE is a stringent test case for compressive sensing because a significant amount of effort has been expended developing advanced model building techniques, which have been implemented in sophisticated general-purpose computer codes. [15][16][17][21][22][23][24][25] …”

Section: 20mentioning

confidence: 99%

“…We note here that the Bregman and split Bregman iterations contain additional noise-filtering steps [Eqs. (15) and (20)] which add back the residual to the residual of the next iteration. As a result, the optimal value of µ will in general vary between the different ℓ 1 optimization approaches, even though the solutions and the predictive errors are practically the same.…”

Section: E Effect Of Noise and Its Relation To Optimal µmentioning

confidence: 99%

Compressive sensing as a paradigm for building physics models

et al. 2013

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The widely-accepted intuition that the important properties of solids are determined by a few key variables underpins many methods in physics. Though this reductionist paradigm is applicable in many physical problems, its utility can be limited because the intuition for identifying the key variables often does not exist or is difficult to develop. Machine learning algorithms (genetic programming, neural networks, Bayesian methods, etc.) attempt to eliminate the a priori need for such intuition but often do so with increased computational burden and human time. A recentlydeveloped technique in the field of signal processing, compressive sensing (CS), provides a simple, general, and efficient way of finding the key descriptive variables. CS is a new paradigm for model building-we show that its models are more physical and predict more accurately than current state-of-the-art approaches, and can be constructed at a fraction of the computational cost and user effort.

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“…39 Jansen and Popa 40 have recently used a related method to calculate the lateral interaction energies of adsorbates on a surface. Their method is equivalent to using a single-width regularization function with a fixed small value for ␥.…”

Section: Related Methodsmentioning

confidence: 99%

Bayesian approach to cluster expansions

2009

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Cluster expansions have proven to be a valuable tool in alloy theory and other problems in materials science but the generation of cluster expansions can be a computationally expensive and time-consuming process. We present a Bayesian framework for developing cluster expansions that explicitly incorporates physical insight into the fitting procedure. We demonstrate how existing methods fit within this framework and use the framework to develop methods that significantly improve the predictive power of cluster expansions for a given training set size. The key to the methods is to apply physical insight and cross validation to develop physically meaningful prior probability distributions for the cluster expansion coefficients. We use the Bayesian approach to develop an efficient method for generating cluster expansions for low-symmetry systems such as surfaces and nanoparticles.

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Bayesian approach to the calculation of lateral interactions: NO/Rh(111)

Cited by 21 publications

References 37 publications

Formation of ordered structures of NO on Rh(111)

Formation of ordered structures of NO on Rh(111)

Compressive sensing as a paradigm for building physics models

Bayesian approach to cluster expansions

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