Machinelearning methods for structure prediction of multicomponent perovskites
Subproject P09
The connection between the composition and function of complex multicomponent oxides is intricate, and our knowledge about it is extremely limited. Current models can at most predict the stability of a stoichiometric composition, a very general structural feature. P09 will develop accelerated ML models to predict the structural details that determine the functionality of perovskites. We will implement two approaches:
First, EAs will be combined with an NN potential trained on the fly to quickly explore the energy landscape of perovskite surfaces and predict their detailed structures. In collaboration with experimental partners (P02 Diebold, P04 Parkinson), those structures will be falsified by direct comparison with diffraction data on existing surfaces. Additionally, the implementation, inputs, and results of the machinelearned force fields (MLFFs) will be shared with the theoretical partners for crossvalidation.
Second, GANs will be trained on known compositions to identify the key features of real perovskite structures and propose new stable ones.
Expertise
We develop and apply atomistic models for theoretical chemistry and materials science. Our expertise covers both classical and quantum methods, as well as multiscale calculations and machinelearning techniques. The group has taken part in the development and public release of a range of packages for atomistic calculations, including:
 WIEN2k, a popular allelectron density functional theory implementation;
 BoltzTraP and BoltzTraP2, two packages used to interpolate electronic band structures and calculate transport coefficients;
 ShengBTE, the first opensource solver of the Boltzmann transport for phonons, which enables predictive calculations of the thermal conductivity of nanostructures;
 almaBTE, a software package for multiscale thermal transport simulation based on first principles;
 Clinamen, an implementation of the covariance matrix adaptation evolutionary algorithm that helps explore complex energy landscapes.
These are some of the methods we have used to study solids, liquids, surfaces, and nanostructures:
 Density functional theory (DFT);
 Classical and abinitio molecular dynamics (MD);
 Selfconsistent anharmonic free energy calculations;
 The Boltzmann transport equation (BTE);
 Traditional and particlefilter Monte Carlo (MC);
 Covariance matrix adaptation evolutionary algorithm (CMAES);
 Classification and regression random forests based on phenomenological information;
 Algorithmically differentiable machinelearning (ML) force fields based on JAX;
 Highthroughput (HT) materials screening.
Team
2021 

MontesCampos, Hadrián; Carrete, Jesús; Varela, Luis M; Madsen, Georg K H A Differentiable NeuralNetwork Force Field for Ionic Liquids Journal Article PrePrint (arXiv:2106.16220), 2021. Abstract  BibTeX  Tags: P09, preprint @article{MontesCampos2021, title = {A Differentiable NeuralNetwork Force Field for Ionic Liquids}, author = {Hadrián MontesCampos and Jesús Carrete and Luis M Varela and Georg K H Madsen}, year = {2021}, date = {20210630}, journal = {PrePrint (arXiv:2106.16220)}, abstract = {We present NeuralIL, a model for the potential energy of an ionic liquid that accurately reproduces firstprinciples results with ordersofmagnitude savings in computational cost. Based on a multilayer perceptron and spherical Bessel descriptors of the atomic environments, NeuralIL is implemented in such a way as to be fully automatically differentiable. It can thus be trained on abinitio forces instead of just energies, to make the most out of the available data, and can efficiently predict arbitrary derivatives of the potential energy. We parametrize the model for the case of ethylammonium nitrate. We discuss the best way to include chemical information in the atomcentered descriptors for a manycomponent system. Furthermore, we demonstrate an ensemblelearning approach to the detection of extrapolation. With outofsample accuracies better than 0.1 kcal/mol in the energies and 100 meV/Å in the forces, our potential model considerably outperforms molecularmechanics force fields and opens the door to largescale thermodynamical calculations with abinitiolike accuracy for ionic liquids. Including the forces does away with the idea that vast amounts of atomic configurations are required to train a neural network force field based on atomcentered descriptors. We also find that a separate treatment of longrange interactions is not required to achieve a highquality representation of the potential energy surface of these dense ionic systems.}, keywords = {P09, preprint}, pubstate = {published}, tppubtype = {article} } We present NeuralIL, a model for the potential energy of an ionic liquid that accurately reproduces firstprinciples results with ordersofmagnitude savings in computational cost. Based on a multilayer perceptron and spherical Bessel descriptors of the atomic environments, NeuralIL is implemented in such a way as to be fully automatically differentiable. It can thus be trained on abinitio forces instead of just energies, to make the most out of the available data, and can efficiently predict arbitrary derivatives of the potential energy. We parametrize the model for the case of ethylammonium nitrate. We discuss the best way to include chemical information in the atomcentered descriptors for a manycomponent system. Furthermore, we demonstrate an ensemblelearning approach to the detection of extrapolation. With outofsample accuracies better than 0.1 kcal/mol in the energies and 100 meV/Å in the forces, our potential model considerably outperforms molecularmechanics force fields and opens the door to largescale thermodynamical calculations with abinitiolike accuracy for ionic liquids. Including the forces does away with the idea that vast amounts of atomic configurations are required to train a neural network force field based on atomcentered descriptors. We also find that a separate treatment of longrange interactions is not required to achieve a highquality representation of the potential energy surface of these dense ionic systems.  
Arrigoni, Marco; Madsen, Georg K H Evolutionary computing and machine learning for discovering of lowenergy defect configurations Journal Article npj Computational Materials, 7 (1), 2021. Abstract  Links  BibTeX  Tags: P09, preTACO @article{Arrigoni2021, title = {Evolutionary computing and machine learning for discovering of lowenergy defect configurations}, author = {Marco Arrigoni and Georg K H Madsen}, doi = {10.1038/s41524021005371}, year = {2021}, date = {20210520}, journal = {npj Computational Materials}, volume = {7}, number = {1}, publisher = {Springer Science and Business Media LLC}, abstract = {Density functional theory (DFT) has become a standard tool for the study of point defects in materials. However, finding the most stable defective structures remains a very challenging task as it involves the solution of a multimodal optimization problem with a highdimensional objective function. Hitherto, the approaches most commonly used to tackle this problem have been mostly empirical, heuristic, and/or based on domain knowledge. In this contribution, we describe an approach for exploring the potential energy surface (PES) based on the covariance matrix adaptation evolution strategy (CMAES) and supervised and unsupervised machine learning models. The resulting algorithm depends only on a limited set of physically interpretable hyperparameters and the approach offers a systematic way for finding lowenergy configurations of isolated point defects in solids. We demonstrate its applicability on different systems and show its ability to find known lowenergy structures and discover additional ones as well.}, keywords = {P09, preTACO}, pubstate = {published}, tppubtype = {article} } Density functional theory (DFT) has become a standard tool for the study of point defects in materials. However, finding the most stable defective structures remains a very challenging task as it involves the solution of a multimodal optimization problem with a highdimensional objective function. Hitherto, the approaches most commonly used to tackle this problem have been mostly empirical, heuristic, and/or based on domain knowledge. In this contribution, we describe an approach for exploring the potential energy surface (PES) based on the covariance matrix adaptation evolution strategy (CMAES) and supervised and unsupervised machine learning models. The resulting algorithm depends only on a limited set of physically interpretable hyperparameters and the approach offers a systematic way for finding lowenergy configurations of isolated point defects in solids. We demonstrate its applicability on different systems and show its ability to find known lowenergy structures and discover additional ones as well.  
2020 

van Roekeghem, Ambroise; Carrete, Jesús; Curtarolo, Stefano; Mingo, Natalio Highthroughput study of the static dielectric constant at high temperatures in oxide and fluoride cubic perovskites Journal Article Physical Review Materials, 4 (11), pp. 113804, 2020. Abstract  Links  BibTeX  Tags: P09, preTACO @article{Roekeghem2020, title = {Highthroughput study of the static dielectric constant at high temperatures in oxide and fluoride cubic perovskites}, author = {Ambroise van Roekeghem and Jesús Carrete and Stefano Curtarolo and Natalio Mingo}, doi = {10.1103/physrevmaterials.4.113804}, year = {2020}, date = {20201113}, journal = {Physical Review Materials}, volume = {4}, number = {11}, pages = {113804}, publisher = {American Physical Society (APS)}, abstract = {Using finitetemperature phonon calculations and the LyddaneSachsTeller relations, we calculate ab initio the static dielectric constants of 78 semiconducting oxides and fluorides with cubic perovskite structures at 1000 K. We first compare our method with experimental measurements, and we find that it succeeds in describing the temperature dependence and the relative ordering of the static dielectric constant ε_{DC} in the series of oxides BaTiO_{3}, SrTiO_{3}, KTaO_{3}. We show that the effects of anharmonicity on the ionclamped dielectric constant, on Born charges, and on phonon lifetimes, can be neglected in the framework of our highthroughput study. Based on the hightemperature phonon spectra, we find that the dispersion of ε_{DC} is one order of magnitude larger among oxides than fluorides at 1000 K. We display the correlograms of the dielectric constants with simple structural descriptors, and we point out that ε_{DC} is actually well correlated with the infinitefrequency dielectric constant ε_{∞}, even in those materials with phase transitions in which ε_{DC} is strongly temperature dependent.}, keywords = {P09, preTACO}, pubstate = {published}, tppubtype = {article} } Using finitetemperature phonon calculations and the LyddaneSachsTeller relations, we calculate ab initio the static dielectric constants of 78 semiconducting oxides and fluorides with cubic perovskite structures at 1000 K. We first compare our method with experimental measurements, and we find that it succeeds in describing the temperature dependence and the relative ordering of the static dielectric constant ε_{DC} in the series of oxides BaTiO_{3}, SrTiO_{3}, KTaO_{3}. We show that the effects of anharmonicity on the ionclamped dielectric constant, on Born charges, and on phonon lifetimes, can be neglected in the framework of our highthroughput study. Based on the hightemperature phonon spectra, we find that the dispersion of ε_{DC} is one order of magnitude larger among oxides than fluorides at 1000 K. We display the correlograms of the dielectric constants with simple structural descriptors, and we point out that ε_{DC} is actually well correlated with the infinitefrequency dielectric constant ε_{∞}, even in those materials with phase transitions in which ε_{DC} is strongly temperature dependent.  
2017 

Legrain, Fleur; Carrete, Jesús; van Roekeghem, Ambroise; Curtarolo, Stefano; Mingo, Natalio How Chemical Composition Alone Can Predict Vibrational Free Energies and Entropies of Solids Journal Article Chemistry of Materials, 29 (15), pp. 6220–6227, 2017. Abstract  Links  BibTeX  Tags: P09, preTACO @article{Legrain2017, title = {How Chemical Composition Alone Can Predict Vibrational Free Energies and Entropies of Solids}, author = {Fleur Legrain and Jesús Carrete and Ambroise van Roekeghem and Stefano Curtarolo and Natalio Mingo}, doi = {10.1021/acs.chemmater.7b00789}, year = {2017}, date = {20170622}, journal = {Chemistry of Materials}, volume = {29}, number = {15}, pages = {62206227}, publisher = {American Chemical Society (ACS)}, abstract = {Computing vibrational free energies (F_{vib}) and entropies (S_{vib}) has posed a longstanding challenge to the highthroughput ab initio investigation of finite temperature properties of solids. Here, we use machinelearning techniques to efficiently predict F_{vib} and S_{vib} of crystalline compounds in the Inorganic Crystal Structure Database. Using descriptors based simply on the chemical formula and using a training set of only 300 compounds, mean absolute errors of less than 0.04 meV/K/atom (15 meV/atom) are achieved for S_{vib} (F_{vib}), whose values are distributed within a range of 0.9 meV/K/atom (300 meV/atom.) In addition, for training sets containing fewer than 2000 compounds, the chemical formula alone is shown to perform as well as, if not better than, four other more complex descriptors previously used in the literature. The accuracy and simplicity of the approach means that it can be advantageously used for fast screening of chemical reactions at finite temperatures.}, keywords = {P09, preTACO}, pubstate = {published}, tppubtype = {article} } Computing vibrational free energies (F_{vib}) and entropies (S_{vib}) has posed a longstanding challenge to the highthroughput ab initio investigation of finite temperature properties of solids. Here, we use machinelearning techniques to efficiently predict F_{vib} and S_{vib} of crystalline compounds in the Inorganic Crystal Structure Database. Using descriptors based simply on the chemical formula and using a training set of only 300 compounds, mean absolute errors of less than 0.04 meV/K/atom (15 meV/atom) are achieved for S_{vib} (F_{vib}), whose values are distributed within a range of 0.9 meV/K/atom (300 meV/atom.) In addition, for training sets containing fewer than 2000 compounds, the chemical formula alone is shown to perform as well as, if not better than, four other more complex descriptors previously used in the literature. The accuracy and simplicity of the approach means that it can be advantageously used for fast screening of chemical reactions at finite temperatures.  
2016 

van Roekeghem, Ambroise; Carrete, Jesús; Oses, Corey; Curtarolo, Stefano; Mingo, Natalio HighThroughput Computation of Thermal Conductivity of HighTemperature Solid Phases: The Case of Oxide and Fluoride Perovskites Journal Article Physical Review X, 6 (4), pp. 041061, 2016. Abstract  Links  BibTeX  Tags: P09, preTACO @article{Roekeghem2016, title = {HighThroughput Computation of Thermal Conductivity of HighTemperature Solid Phases: The Case of Oxide and Fluoride Perovskites}, author = {Ambroise van Roekeghem and Jesús Carrete and Corey Oses and Stefano Curtarolo and Natalio Mingo}, doi = {10.1103/physrevx.6.041061}, year = {2016}, date = {20160613}, journal = {Physical Review X}, volume = {6}, number = {4}, pages = {041061}, publisher = {American Physical Society (APS)}, abstract = {Using finitetemperature phonon calculations and machinelearning methods, we assess the mechanical stability of about 400 semiconducting oxides and fluorides with cubic perovskite structures at 0, 300, and 1000 K. We find 92 mechanically stable compounds at high temperatures—including 36 not mentioned in the literature so far—for which we calculate the thermal conductivity. We show that the thermal conductivity is generally smaller in fluorides than in oxides, largely due to a lower ionic charge, and describe simple structural descriptors that are correlated with its magnitude. Furthermore, we show that the thermal conductivities of most cubic perovskites decrease more slowly than the usual T^{−1} behavior. Within this set, we also screen for materials exhibiting negative thermal expansion. Finally, we describe a strategy to accelerate the discovery of mechanically stable compounds at high temperatures.}, keywords = {P09, preTACO}, pubstate = {published}, tppubtype = {article} } Using finitetemperature phonon calculations and machinelearning methods, we assess the mechanical stability of about 400 semiconducting oxides and fluorides with cubic perovskite structures at 0, 300, and 1000 K. We find 92 mechanically stable compounds at high temperatures—including 36 not mentioned in the literature so far—for which we calculate the thermal conductivity. We show that the thermal conductivity is generally smaller in fluorides than in oxides, largely due to a lower ionic charge, and describe simple structural descriptors that are correlated with its magnitude. Furthermore, we show that the thermal conductivities of most cubic perovskites decrease more slowly than the usual T^{−1} behavior. Within this set, we also screen for materials exhibiting negative thermal expansion. Finally, we describe a strategy to accelerate the discovery of mechanically stable compounds at high temperatures. 