5 research outputs found
Building nonparametric -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
governing the interaction order modelled. The order 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 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
Similarity between Amorphous and Crystalline Phases: The Case of TiO<inf>2</inf>
Amorphous and crystalline materials differ in their long-range structural order. On the other hand, short-range order in amorphous and crystalline materials often appears similar. Here, we use a recently introduced method for obtaining quantitative measures for structural similarity to compare crystalline and amorphous materials. We compare seven common crystalline polymorphs of TiO2, all assembled out of TiO6 or TiO7 polyhedral building blocks, to liquid and amorphous TiO2 in a quantitative two-dimensional similarity plot. We find high structural similarity between a model of amorphous TiO2, obtained by ab initio molecular-dynamics, and the B-TiO2 crystalline polymorph. The general approach presented here sheds new light on a long-standing controversy in the structural theory of amorphous solids