Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

Central Odontogenic Fibroma of Simple Type

Central odontogenic fibroma (COF) is an extremely rare benign tumor that accounts for 0.1% of all odontogenic tumors. It is a lesion associated with the crown of an unerupted tooth resembling dentigerous cyst. In this report, a 10-year-old male patient is presented, who was diagnosed with central odontogenic fibroma of simple type from clinical, radiological, and histopathological findings

Molecular characterization of old local grapevine varieties from South East European countries

South East European (SEE) viticulture partially relies on native grapevine varieties, previously scarcely described. In order to characterize old local grapevine varieties and assess the level of synonymy and genetic diversity from SEE countries, we described and genotyped 122 accessions from Albania, Federation of Bosnia and Herzegovina (B&H), Croatia, Macedonia, Moldova, Montenegro, Republika Srpska (Bosnia and Herzegovina) and Romania on nine most commonly used microsatellite loci. As a result of the study a total of 86 different genotypes were identified. All loci were very polymorphic and a total of 96 alleles were detected, ranging from 8 to 14 alleles per locus, with an average allele number of 10.67. Overall observed heterozygosity was 0.759 and slightly lower than expected (0.789) while gene diversity per locus varied between 0.600 (VVMD27) and 0.906 (VVMD28). Eleven cases of synonymy and three of homonymy have been recorded for samples harvested from different countries. Cultivars with identical genotypes were mostly detected between neighboring countries. No clear differentiation between countries was detected although several specific alleles were detected. The integration of the obtained genetic data with ampelographic ones is very important for accurate identification of the SEE cultivars and provides a significant tool in cultivar preservation and utilization.

Developing an interatomic potential for martensitic phase transformations in zirconium by machine learning

Interatomic potentials: predicting phase transformations in zirconium Machine learning leads to a new interatomic potential for zirconium that can predict phase transformations. A team led by Hongxian Zong at Xi’an Jiaotong University, China, and Turab Lookman at Los Alamos National Laboratory, U.S.A, used a Gaussian-type machine learning approach to produce an interatomic potential that predicted phase transformations in zirconium. They expressed each atomic energy contribution via changes in the local atomic environment, such as bond length, shape, and volume. The resulting machine-learning potential successfully described pure zirconium’s physical properties. When used in molecular dynamics simulations, it predicted a zirconium phase diagram as a function of both temperature and pressure that agreed well with previous experiments and simulations. Developing learnt interatomic potentials in phase-transforming systems could help us better simulate complex systems

Understanding high pressure hydrogen with a hierarchical machine-learned potential

The hydrogen phase diagram has a number of unusual features which are generally well reproduced by density functional calculations. Unfortunately, these calculations fail to provide good physical insights into why those features occur. In this paper, we parameterize a model potential for molecular hydrogen which permits long and large simulations. The model shows excellent reproduction of the phase diagram, including the broken-symmetry Phase II, an efficiently-packed phase III and the maximum in the melt curve. It also gives an excellent reproduction of the vibrational frequencies, including the maximum in the vibrational frequency $\nu(P)$ and negative thermal expansion. By detailed study of lengthy molecular dynamics, we give intuitive explanations for observed and calculated properties. All solid structures approximate to hexagonal close packed, with symmetry broken by molecular orientation. At high pressure, Phase I shows significant short-ranged correlations between molecular orientations. The turnover in Raman frequency is due to increased coupling between neighboring molecules, rather than weakening of the bond. The liquid is denser than the close-packed solid because, at molecular separations below 2.3\AA, the favoured relative orientation switches from quadrupole-energy-minimising to steric-repulsion-minimising. The latter allows molecules to get closer together, without atoms getting closer but this cannot be achieved within the constraints of a close-packed layer