62,774 research outputs found
Machine-learning of atomic-scale properties based on physical principles
We briefly summarize the kernel regression approach, as used recently in
materials modelling, to fitting functions, particularly potential energy
surfaces, and highlight how the linear algebra framework can be used to both
predict and train from linear functionals of the potential energy, such as the
total energy and atomic forces. We then give a detailed account of the Smooth
Overlap of Atomic Positions (SOAP) representation and kernel, showing how it
arises from an abstract representation of smooth atomic densities, and how it
is related to several popular density-based representations of atomic
structure. We also discuss recent generalisations that allow fine control of
correlations between different atomic species, prediction and fitting of
tensorial properties, and also how to construct structural kernels---applicable
to comparing entire molecules or periodic systems---that go beyond an additive
combination of local environments
Detecting periodic time scales in temporal networks
Temporal networks are commonly used to represent dynamical complex systems
like social networks, simultaneous firing of neurons, human mobility or public
transportation. Their dynamics may evolve on multiple time scales
characterising for instance periodic activity patterns or structural changes.
The detection of these time scales can be challenging from the direct
observation of simple dynamical network properties like the activity of nodes
or the density of links. Here we propose two new methods, which rely on already
established static representations of temporal networks, namely supra-adjacency
matrices and temporal event graphs. We define dissimilarity metrics extracted
from these representations and compute their Fourier Transform to effectively
identify dominant periodic time scales characterising the original temporal
network. We demonstrate our methods using synthetic and real-world data sets
describing various kinds of temporal networks. We find that while in all cases
the two methods outperform the reference measures, the supra-adjacency based
method identifies more easily periodic changes in network density, while the
temporal event graph based method is better suited to detect periodic changes
in the group structure of the network. Our methodology may provide insights
into different phenomena occurring at multiple time-scales in systems
represented by temporal networks.Comment: 19 pages, 11 figure
Alchemical and structural distribution based representation for improved QML
We introduce a representation of any atom in any chemical environment for the
generation of efficient quantum machine learning (QML) models of common
electronic ground-state properties. The representation is based on scaled
distribution functions explicitly accounting for elemental and structural
degrees of freedom. Resulting QML models afford very favorable learning curves
for properties of out-of-sample systems including organic molecules,
non-covalently bonded protein side-chains, (HO)-clusters, as well as
diverse crystals. The elemental components help to lower the learning curves,
and, through interpolation across the periodic table, even enable "alchemical
extrapolation" to covalent bonding between elements not part of training, as
evinced for single, double, and triple bonds among main-group elements
Crystal Structure Representations for Machine Learning Models of Formation Energies
We introduce and evaluate a set of feature vector representations of crystal
structures for machine learning (ML) models of formation energies of solids. ML
models of atomization energies of organic molecules have been successful using
a Coulomb matrix representation of the molecule. We consider three ways to
generalize such representations to periodic systems: (i) a matrix where each
element is related to the Ewald sum of the electrostatic interaction between
two different atoms in the unit cell repeated over the lattice; (ii) an
extended Coulomb-like matrix that takes into account a number of neighboring
unit cells; and (iii) an Ansatz that mimics the periodicity and the basic
features of the elements in the Ewald sum matrix by using a sine function of
the crystal coordinates of the atoms. The representations are compared for a
Laplacian kernel with Manhattan norm, trained to reproduce formation energies
using a data set of 3938 crystal structures obtained from the Materials
Project. For training sets consisting of 3000 crystals, the generalization
error in predicting formation energies of new structures corresponds to (i)
0.49, (ii) 0.64, and (iii) 0.37 eV/atom for the respective representations
Alchemical and structural distribution based representation for improved QML
We introduce a representation of any atom in any chemical environment for the
generation of efficient quantum machine learning (QML) models of common
electronic ground-state properties. The representation is based on scaled
distribution functions explicitly accounting for elemental and structural
degrees of freedom. Resulting QML models afford very favorable learning curves
for properties of out-of-sample systems including organic molecules,
non-covalently bonded protein side-chains, (HO)-clusters, as well as
diverse crystals. The elemental components help to lower the learning curves,
and, through interpolation across the periodic table, even enable "alchemical
extrapolation" to covalent bonding between elements not part of training, as
evinced for single, double, and triple bonds among main-group elements
Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning
Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, sometimes by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We review, discuss and benchmark state-of-the-art representations and relations between them, including smooth overlap of atomic positions, many-body tensor representation, and symmetry functions. For this, we use a unified mathematical framework based on many-body functions, group averaging and tensor products, and compare energy predictions for organic molecules, binary alloys and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method and hyper-parameter optimization
Structural and electronic properties of p-doped silicon clathrates
We present an ab initio study of the structural and electronic properties of type-I and type-II silicon clathrates doped by elements chosen to be more electronegative than silicon. Depending on the intercalated element, we show that the electronic properties of doped silicon clathrates can exhibit metallic, semiconducting, or insulating behavior. It is found in particular that doping can lead to silicon-based materials with a band gap in the visible range and that, in type-II clathrates, the gap can be direct. However, the analysis of the selection rules show that the optical transitions are forbidden in type-I and type-II clathrates. Concerning the structural properties, the bonding between the dopant atom and silicon can significantly decrease the compressibility of the host network to values equivalent to the one of the much denser diamond phase. The present results are complemented and rationalized by the study of endohedrally doped SinHn n=20,24,28 silicon clusters
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