One of the most exciting tools that have entered the material science toolbox in recent years is machine learning. This collection of statistical methods has already proved to be capable of considerably speeding up both fundamental and applied research. At present, we are witnessing an explosion of works that develop and apply machine learning to solid-state systems. We provide a comprehensive overview and analysis of the most recent research in this topic. As a starting point, we introduce machine learning principles, algorithms, descriptors, and databases in materials science. We continue with the description of different machine learning approaches for the discovery of stable materials and the prediction of their crystal structure. Then we discuss research in numerous quantitative structure–property relationships and various approaches for the replacement of first-principle methods by machine learning. We review how active learning and surrogate-based optimization can be applied to improve the rational design process and related examples of applications. Two major questions are always the interpretability of and the physical understanding gained from machine learning models. We consider therefore the different facets of interpretability and their importance in materials science. Finally, we propose solutions and future research paths for various challenges in computational materials science.

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Recent advances and applications of machine learning in solid-state materials science

Propelled partly by the Materials Genome Initiative, and partly by the algorithmic developments and the resounding successes of data-driven efforts in other domains, informatics strategies are beginning to take shape within materials science. These approaches lead to surrogate machine learning models that enable rapid predictions based purely on past data rather than by direct experimentation or by computations/simulations in which fundamental equations are explicitly solved. Data-centric informatics methods are becoming useful to determine material properties that are hard to measure or compute using traditional methods—due to the cost, time or effort involved—but for which reliable data either already exists or can be generated for at least a subset of the critical cases. Predictions are typically interpolative, involving fingerprinting a material numerically first, and then following a mapping (established via a learning algorithm) between the fingerprint and the property of interest. Fingerprints, also referred to as “descriptors”, may be of many types and scales, as dictated by the application domain and needs. Predictions may also be extrapolative—extending into new materials spaces—provided prediction uncertainties are properly taken into account. This article attempts to provide an overview of some of the recent successful data-driven “materials informatics” strategies undertaken in the last decade, with particular emphasis on the fingerprint or descriptor choices. The review also identifies some challenges the community is facing and those that should be overcome in the near future.

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Machine learning in materials informatics: recent applications and prospects

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.Machine learning allows electronic structure calculations to access larger system sizes and, in dynamical simulations, longer time scales. Here, the authors perform such a simulation using a machine-learned density functional that avoids direct solution of the Kohn-Sham equations.

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Bypassing the Kohn-Sham equations with machine learning

Recent advances in experimental and computational methods are increasing the quantity and complexity of generated data. This massive amount of raw data needs to be stored and interpreted in order to advance the materials science field. Identifying correlations and patterns from large amounts of complex data is being performed by machine learning (ML) algorithms for decades. Recently, the materials science community started to invest in these methodologies to extract knowledge and insights from the accumulated data. This review follows a logical sequence starting from density functional theory (DFT) as the representative instance of electronic structure methods, to the subsequent high-throughput (HT) approach, used to generate large amounts of data. Ultimately, data-driven strategies which include data mining, screening, and machine learning techniques, employ the data generated. We show how these approaches to modern computational materials science are being used to uncover complexities and design novel materials with enhanced properties. Finally, we point to the present research problems, challenges, and potential future perspectives of this new exciting field.

https://iopscience.iop.org/article/10.1088/2515-7639/ab084b/pdf

From DFT to machine learning: recent approaches to materials science–a review

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of \textit{ab initio} calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to \emph{ab initio} methods, \emph{i.e.} nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost.

Machine Learning of Molecular Electronic Properties in Chemical Compound Space

Using a one-dimensional model, we explore the ability of machine learning to approximate the non-interacting kinetic energy density functional of diatomics. This nonlinear interpolation between Kohn-Sham reference calculations can (i) accurately dissociate a diatomic, (ii) be systematically improved with increased reference data and (iii) generate accurate self-consistent densities via a projection method that avoids directions with no data. With relatively few densities, the error due to the interpolation is smaller than typical errors in standard exchange-correlation functionals.

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Orbital-free bond breaking via machine learning

Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly accurate self-consistent densities and molecular forces are found, indicating the possibility for ab-initio molecular dynamics simulations.

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Leo Blooston

Papers

Orbital-free bond breaking via machine learning

Orbital-free Bond Breaking via Machine Learning