4,697 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
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
SchNet - a deep learning architecture for molecules and materials
Deep learning has led to a paradigm shift in artificial intelligence,
including web, text and image search, speech recognition, as well as
bioinformatics, with growing impact in chemical physics. Machine learning in
general and deep learning in particular is ideally suited for representing
quantum-mechanical interactions, enabling to model nonlinear potential-energy
surfaces or enhancing the exploration of chemical compound space. Here we
present the deep learning architecture SchNet that is specifically designed to
model atomistic systems by making use of continuous-filter convolutional
layers. We demonstrate the capabilities of SchNet by accurately predicting a
range of properties across chemical space for \emph{molecules and materials}
where our model learns chemically plausible embeddings of atom types across the
periodic table. Finally, we employ SchNet to predict potential-energy surfaces
and energy-conserving force fields for molecular dynamics simulations of small
molecules and perform an exemplary study of the quantum-mechanical properties
of C-fullerene that would have been infeasible with regular ab initio
molecular dynamics
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