Incompleteness of Atomic Structure Representations

Pozdnyakov, Sergey; Willatt, Michael J.; Bartók, Albert P.; Ortner, Christoph; Csänyi, Gábor; Ceriotti, Michele

doi:10.1103/physrevlett.125.166001

Cited by 159 publications

(176 citation statements)

References 41 publications

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“…Recently, however, it was discovered that neither SOAP nor the other equivalent descriptors are complete, and counter-examples were shown also for the higher-order bispectrum (which corresponds to four-body correlations). 71 Therefore, SOAP-based models cannot describe an atomic energy function of its neighborhood to arbitrary precision, although practical successes suggest that the corresponding errors are on the same order or smaller than other systematic errors that are due to locality and k -point sampling (see below for a more detailed discussion of these). Yet, it may well be possible that complete descriptors can lead to more efficient learning; see ref ( 51 ) for more details.…”

Section: Learning Atomistic Propertiesmentioning

confidence: 99%

Gaussian Process Regression for Materials and Molecules

et al. 2021

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We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

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Section: Learning Atomistic Propertiesmentioning

confidence: 99%

Gaussian Process Regression for Materials and Molecules

et al. 2021

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“…We consider three models: a linear multi-scale model; a square kernel model, that is equivalent to using a quadratic functional of the SOAP features, , which incorporates 4 and 5-body correlations and enhance the many-body character of the representation at the local scale; 92 a weighted combination of the two. The learning curves for the trace ( λ = 0) of the polarizability tensor, shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

Multi-scale approach for the prediction of atomic scale properties

2021

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“…Currently, it is also investigated whether representations based on two-body or three-body terms are accurate enough to uniquely identify a molecule. 520 …”

Section: Modelsmentioning

confidence: 99%

Machine Learning for Electronically Excited States of Molecules

2020

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Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

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Incompleteness of Atomic Structure Representations

Abstract: Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.

Cited by 159 publications

References 41 publications

Gaussian Process Regression for Materials and Molecules

Gaussian Process Regression for Materials and Molecules

Multi-scale approach for the prediction of atomic scale properties

Machine Learning for Electronically Excited States of Molecules

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