9,663 research outputs found
Atomic-scale representation and statistical learning of tensorial properties
This chapter discusses the importance of incorporating three-dimensional
symmetries in the context of statistical learning models geared towards the
interpolation of the tensorial properties of atomic-scale structures. We focus
on Gaussian process regression, and in particular on the construction of
structural representations, and the associated kernel functions, that are
endowed with the geometric covariance properties compatible with those of the
learning targets. We summarize the general formulation of such a
symmetry-adapted Gaussian process regression model, and how it can be
implemented based on a scheme that generalizes the popular smooth overlap of
atomic positions representation. We give examples of the performance of this
framework when learning the polarizability and the ground-state electron
density of a molecule
sGDML: Constructing Accurate and Data Efficient Molecular Force Fields Using Machine Learning
We present an optimized implementation of the recently proposed symmetric
gradient domain machine learning (sGDML) model. The sGDML model is able to
faithfully reproduce global potential energy surfaces (PES) for molecules with
a few dozen atoms from a limited number of user-provided reference molecular
conformations and the associated atomic forces. Here, we introduce a Python
software package to reconstruct and evaluate custom sGDML force fields (FFs),
without requiring in-depth knowledge about the details of the model. A
user-friendly command-line interface offers assistance through the complete
process of model creation, in an effort to make this novel machine learning
approach accessible to broad practitioners. Our paper serves as a
documentation, but also includes a practical application example of how to
reconstruct and use a PBE0+MBD FF for paracetamol. Finally, we show how to
interface sGDML with the FF simulation engines ASE (Larsen et al., J. Phys.
Condens. Matter 29, 273002 (2017)) and i-PI (Kapil et al., Comput. Phys.
Commun. 236, 214-223 (2019)) to run numerical experiments, including structure
optimization, classical and path integral molecular dynamics and nudged elastic
band calculations
Marriages of Mathematics and Physics: A Challenge for Biology
The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences
Efficient approach for simulating distorted materials
The operation principles of nanoscale devices are based upon both electronic
and mechanical properties of materials. Because these properties can be
coupled, they need to be investigated simultaneously. At this moment, however,
the electronic structure calculations with custom-made long-range mechanical
distortions are impossible, or expensive at best. Here we present a unified
formalism to solve exactly the electronic structures of nanomaterials with
versatile distortions. We illustrate the formalism by investigating twisted
armchair graphene nanoribbons with the least possible number of atoms. Apart
from enabling versatile material distortions, the formalism is capable of
reducing computational costs orders of magnitude in various areas of science
and engineering.Comment: 4 pages, 2 figures, 2 table
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
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