scholarly journals Identifying Domains of Applicability of Machine Learning Models for Materials Science

2019 ◽  
Author(s):  
Christopher Sutton ◽  
Mario Boley ◽  
Luca M. Ghiringhelli ◽  
Matthias Rupp ◽  
Jilles Vreeken ◽  
...  
Keyword(s):  
Machine Learning ◽  
Ground State ◽  
Materials Science ◽  
Many Body ◽  
Simple Set ◽  
Domain Of Applicability ◽  
N Gram ◽  
The Many ◽  
Error Statistic ◽  
Machine Learning Models

We present an extension to the usual machine learning process that allows for the identification of the domain of applicability of a fitted model, i.e., the region in its domain where it performs most accurately. This approach is applied to several vastly different but commonly used materials representations (namely the n-gram approach, SOAP, and the many body tenor representation), which are practically indistinguishable based on performance using a single error statistic. Moreover, these models appear unsatisfactory for screening applications as they fail to reliably identify the ground state polymorphs. When applying our newly developed analysis for each of the models, we can identify the domain of applicability for each model according to a simple set of interpretable conditions. We show that identification of the domain of applicability in the prediction of the formation energy enables a more accurate ground-state search - a crucial step for the discovery of novel materials.

scholarly journals Identifying Domains of Applicability of Machine Learning Models for Materials Science

2019 ◽  
Author(s):  
Christopher Sutton ◽  
Mario Boley ◽  
Luca M. Ghiringhelli ◽  
Matthias Rupp ◽  
Jilles Vreek ◽  
...  
Keyword(s):  
Machine Learning ◽  
Ground State ◽  
Materials Science ◽  
Many Body ◽  
Simple Set ◽  
Domain Of Applicability ◽  
N Gram ◽  
The Many ◽  
Error Statistic ◽  
Machine Learning Models

We present an extension to the usual machine learning process that allows for the identification of the domain of applicability of a fitted model, i.e., the region in its domain where it performs most accurately. This approach is applied to several vastly different but commonly used materials representations (namely the n-gram approach, SOAP, and the many body tenor representation), which are practically indistinguishable based on performance using a single error statistic. Moreover, these models appear unsatisfactory for screening applications as they fail to reliably identify the ground state polymorphs. When applying our newly developed analysis for each of the models, we can identify the domain of applicability for each model according to a simple set of interpretable conditions. We show that identification of the domain of applicability in the prediction of the formation energy enables a more accurate ground-state search - a crucial step for the discovery of novel materials.

scholarly journals Identifying Domains of Applicability of Machine Learning Models for Materials Science

2019 ◽  
Author(s):  
Christopher Sutton ◽  
Mario Boley ◽  
Luca M. Ghiringhelli ◽  
Matthias Rupp ◽  
Jilles Vreeken ◽  
...  
Keyword(s):  
Machine Learning ◽  
Ground State ◽  
Materials Science ◽  
Many Body ◽  
Simple Set ◽  
Domain Of Applicability ◽  
N Gram ◽  
The Many ◽  
Error Statistic ◽  
Machine Learning Models

We present an extension to the usual machine learning process that allows for the identification of the domain of applicability of a fitted model, i.e., the region in its domain where it performs most accurately. This approach is applied to several vastly different but commonly used materials representations (namely the n-gram approach, SOAP, and the many body tenor representation), which are practically indistinguishable based on performance using a single error statistic. Moreover, these models appear unsatisfactory for screening applications as they fail to reliably identify the ground state polymorphs. When applying our newly developed analysis for each of the models, we can identify the domain of applicability for each model according to a simple set of interpretable conditions. We show that identification of the domain of applicability in the prediction of the formation energy enables a more accurate ground-state search - a crucial step for the discovery of novel materials.

scholarly journals Opportunities and Challenges for Machine Learning in Materials Science

2020 ◽  
Vol 50 (1) ◽  
pp. 71-103
Author(s):  
Dane Morgan ◽  
Ryan Jacobs
Keyword(s):  
Machine Learning ◽  
Best Practices ◽  
Materials Science ◽  
Molecular Simulations ◽  
Learning Models ◽  
Novel Materials ◽  
Domain Of Applicability ◽  
Rapid Changes ◽  
To Come ◽  
Machine Learning Models

Advances in machine learning have impacted myriad areas of materials science, such as the discovery of novel materials and the improvement of molecular simulations, with likely many more important developments to come. Given the rapid changes in this field, it is challenging to understand both the breadth of opportunities and the best practices for their use. In this review, we address aspects of both problems by providing an overview of the areas in which machine learning has recently had significant impact in materials science, and then we provide a more detailed discussion on determining the accuracy and domain of applicability of some common types of machine learning models. Finally, we discuss some opportunities and challenges for the materials community to fully utilize the capabilities of machine learning.

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

scholarly journals Non-Hermitian fractional quantum Hall states

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tsuneya Yoshida ◽  
Koji Kudo ◽  
Yasuhiro Hatsugai
Keyword(s):  
Ground State ◽  
Cold Atoms ◽  
Quantum Hall ◽  
Quantum Zeno Effect ◽  
Many Body ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Zeno Effect ◽  
Quantum Hall States ◽  
The Many

AbstractWe demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.

Machine Learning Models for Lipophilicity and Their Domain of Applicability

2007 ◽  
Vol 4 (4) ◽  
pp. 524-538 ◽  
Author(s):  
Timon Schroeter ◽  
Anton Schwaighofer ◽  
Sebastian Mika ◽  
Antonius Ter Laak ◽  
Detlev Suelzle ◽  
...  
Keyword(s):  
Machine Learning ◽  
Learning Models ◽  
Domain Of Applicability ◽  
Machine Learning Models

EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

2011 ◽  
Vol 20 (02) ◽  
pp. 252-258 ◽  
Author(s):  
LUDOVIC BONNEAU ◽  
JULIEN LE BLOAS ◽  
PHILIPPE QUENTIN ◽  
NIKOLAY MINKOV
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Energy Difference ◽  
Pair Type ◽  
Many Body ◽  
Hartree Fock ◽  
Ground State Properties ◽  
Pairing Correlations ◽  
The Many ◽  
The Impact

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

scholarly journals Size-Extensive Molecular Machine Learning with Global Descriptors

2019 ◽  
Author(s):  
Hyunwook Jung ◽  
Sina Stocker ◽  
Christian Kunkel ◽  
Harald Oberhofer ◽  
Byungchan Han ◽  
...  
Keyword(s):  
Machine Learning ◽  
Small Molecules ◽  
Computational Cost ◽  
Many Body ◽  
Training Set ◽  
Large Molecules ◽  
Large Size ◽  
Size Extensivity ◽  
The Many ◽  
Structure Calculations

<div> <div> <div> <p>Machine learning (ML) models are increasingly used to predict molecular prop- erties in a high-throughput setting at a much lower computational cost than con- ventional electronic structure calculations. Such ML models require descriptors that encode the molecular structure in a vector. These descriptors are generally designed to respect the symmetries and invariances of the target property. However, size- extensivity is usually not guaranteed for so-called global descriptors. In this contri- bution, we show how extensivity can be build into ML models with global descriptors such as the Many-Body Tensor Representation. Properties of extensive and non- extensive models for the atomization energy are systematically explored by training on small molecules and testing on small, medium and large molecules. Our result shows that the non-extensive model is only useful in the size-range of its training set, whereas the extensive models provide reasonable predictions across large size differences. Remaining sources of error for the extensive models are discussed. </p> </div> </div> </div>

Wave-number dependence of the static screening function of an interacting electron gas. I. Lowest-order Hartree–Fock corrections

1970 ◽  
Vol 48 (2) ◽  
pp. 155-165 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Coulomb Interaction ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Wave Number ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Static Screening ◽  
Zero Frequency

The lowest-order Hartree–Fock contributions to the zero frequency screening function are examined for an interacting electron gas in its ground state. Computational methods are developed to treat singularities associated with the bare coulomb interaction and vanishing energy denominators of the many-body perturbation expansion. Numerical results are given. The wave-number dependence in the intermediate (k ~ kF) range differs considerably from that of previous estimates.

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