Session B1: Computational Discovery and Design of Novel Materials II

Quantum Machine Learning

Many of the most relevant properties of matter depend explicitly on atomistic detail, rendering a first principles approach mandatory. Due to the combinatorial scaling of possible compositions and structures this precludes systematic high-throughput screening in search of new compounds for all but the simplest system classes and properties. Therefore it is desirable to exploit implicit redundancies, present in repeatedly performed quantum calculations. I will discuss our latest machine learning models of quantum mechanical observables, trained and applied throughout chemical compound space.   

Quantum-Chemical Insights from Deep Tensor Neural Networks

Discovery of novel materials can be guided by searching databases of known structures and properties. Indeed, electronic structure calculations and machine learning have recently been combined aiming towards the goal of accelerated discovery of chemicals with desired properties. However, the design of an appropriate descriptor is critical to the success of these approaches. Here we address this issue with deep neural tensor networks (DTNN): a deep learning approach that is able to learn efficient representations of molecules and materials [1]. The mathematical construction of the DTNN model provides statistically rigorous partitioning of extensive molecular properties into atomic contributions -- a long-standing challenge for quantum-mechanical calculations of molecules. Beyond achieving accurate energy predictions (1 kcal mol$^{-1}$) throughout compositional and configurational space, DTNN provide spatially and chemically resolved insights into quantum-mechanical properties of molecular systems beyond those trivially contained in the training data. Thus, we propose DTNN as a versatile framework for understanding complex quantum-mechanical systems based on high-throughput electronic structure calculations. [1] K. T. Sch\"utt et al., Nat. Comm. (2016).   

Multifidelity Learning Models for Accurate Bandgap Predictions of Solids

We present a multidelity co-kriging statistical learning framework that combines variable-fidelity quantum mechanical calculations of bandgaps to generate a machine-learned model that enables low-cost accurate predictions of the bandgaps at the highest fidelity level. In addition, the adopted Gaussian process regression formulation allows us to predict the underlying uncertainties as a measure of our confidence in the predictions. Using a set of 600 Elpasolite compounds as an example dataset and using semi-local and hybrid exchange correlation functionals within density functional theory as two levels of modelities, we demonstrate the excellent learning performance of the method against actual high fidelity quantum mechanical calculations of the bandgaps. The presented statistical learning method is not restricted to bandgaps or electronic structure methods and extends the utility of high throughput property predictions in a significant way.   

Finding descriptors for material properties from billions of candidates via compressed sensing: accurate prediction of crystal structures and band gaps from only chemical composition

Identifying the key physical parameters (termed descriptor) determining the target material properties is a critical step toward material discovery and rational design. Thus far, systematic methods for the descriptor identification are not well established. In particular, it has been suggested that good descriptors should both yield an accurate prediction and be physically interpretable [L. M. Ghiringhelli,\emph{et al.}, PRL \textbf{114}, 105503 (2015)]. In this talk, we present a systematic scheme for descriptor identification based on sure independent screening [J. Fan and J. Lv, J. R. Statist. Soc. B {\bf 70}, 849 (2008)] and compressed sensing [E. Candès and M. B. Wakin, IEEE Signal Proc. Mag. {\bf 25}, 21 (2008)]. The scheme starts with automatic building of the ``feature spaces'', i.e. all offered candidate descriptors, and the feature space may contain billions of options. The employed combination of sure independent screening and compressed sensing provides an efficient scheme for identifying the best low-dimensional descriptor. The approach is demonstrated for the important problems of crystal-structure and band-gap prediction.   

A machine learning approach for the classification of metallic glasses

Metallic glasses possess an extensive set of mechanical properties along with plastic-like processability [1]. As a result, they are a promising material in many industrial applications [2]. However, the successful synthesis of novel metallic glasses requires trial and error, costing both time and resources. Therefore, we propose a high-throughput approach that combines an extensive set of experimental measurements with advanced machine learning techniques. This allows us to classify metallic glasses and predict the full phase diagrams for a given alloy system. Thus this method provides a means to identify potential glass-formers and opens up the possibility for accelerating and reducing the cost of the design of new metallic glasses. [1] J. Schroers, N. Paton, Amorphous metal alloys form like plastics. Adv. Mater. Processes 164(1), 61-63 (2006) [2] W. L. Johnson, Bulk glass-forming metallic alloys: science and technology. MRS Bull. 24, 42–56 (1999)   

Machine Learning of ABO$_3$ Crystalline Compounds

We apply two advanced machine learning methods to a database of experimentally known AB$O_3$ materials to predict the existence of possible new perovskite materials and possible new cubic perovskites. Constructing a list of 625 possible new materials from charge conserving combinations of A and B atoms in known stable ABO$_3$ materials, we predict about 440 new perovskites. These new perovskites are predicted most likely to occur when the A and B atoms are a lanthanide or actinide, when the A atom is a alkali, alkali earth, or late transition metal, and a when the B atom is a $p$-block atom. These results are in basic agreement with the recent materials discovery by substitution analysis of Hautier et al. [Inorg. Chem. 50, 656 (2011)] who data-mined the entire ICSD data base to develop the probability that in any crystal structure atom X could be substituted for by atom Y. The results of our analysis has several points of disagreement with a recent high throughput DFT study of ABO$_3$ crystalline compounds by Emery et al. [Chem. Mat. 28, 5621 (2016)] who predict few, if any, new perovskites whose A and B atoms are both a lanthanide. They also predict far more new cubic perovskites than we do: We predict few, if any, with a high degree of probability.   

Machine learning energies of 2M elpasolite (ABC$_2$D$_6$) crystals

Elpasolite is one of the most predominant quaternary crystal structures (AlNaK$_2$F$_6$ prototype) reported in the Inorganic Crystal Structure Database. We present a machine learning model to calculate density functional theory quality formation energies for all 2M possible ABC$_2$D$_6$ elpasolite crystals one can make up from all main-group elements up to Bi. The model's accuracy can be improved systematically, reaching a mean-absolute out of sample error of 0.1 eV/atom after training on 10k crystals. Out of the 2M crystals, we have identified 128 new structures which we predict to be on the convex hull---among which NFAl$_2$Ca$_6$, a metallic elpasolite with unusual stoichiometry and negative atomic oxidation state of Al.   

Understanding magnetism in transition-metal multilayer thin-films on MgO(001) by using machine-learning technique

New computational approaches for exploring materials with many exciting properties continue to grow in modern material science. In the field of spin-electronics, however, the effective procedure is still lacking due to a difficulty in treating magnetism, while searching promising ferromagnetic transition-metal (TM) multilayer thin-films with large perpendicular magnetocrystalline anisotropy (MCA) is strongly desired, e.g., for successful magnetic tunnel junction devices. Here, in order to show the underlying trends and physics in the magnetism in multilayer thin-film systems, we carried out first principles calculations by employing six-atomic-layer slabs of Fe and Au (Co and Au) on MgO(001). With an assist of the cluster-expansion method, the magnetic moments are found to follow the Slater-Pauling rule, i.e., governed by composition of the constituent TMs. In contrast, the MCA energy dramatically depends on the atomic-layer alignments with very large variation up to 5 meV/atom-area from a negative value of -2 meV/atom-area. Compressing sensing for understanding such dispersive MCA will be further applied.   

Inferring low-dimensional microstructure representations using convolutional neural networks

We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to provide a high-dimensional characterization of a set of synthetic microstructural images. Next, we use manifold learning to obtain a low-dimensional embedding of this statistical characterization. We show that the low-dimensional embedding extracts the parameters used to generate the images. According to a variety of metrics, the convolutional neural network method yields dramatically better embeddings than the analogous method derived from two-point correlations alone.   

Structure prediction for metastable materials: Sn$_{\mathrm{\mathbf{2}}}$\textbf{N}$_{\mathrm{\mathbf{2}}}$

Recent advances in theoretical structure prediction methods and high-throughput computational techniques are revolutionizing experimental discovery of the thermodynamically stable inorganic materials. Metastable materials represent a new frontier for these studies, since even simple binary non-ground state compounds of common elements may be awaiting discovery. An interesting example of a metastable material is Sn$_{\mathrm{2}}$N$_{\mathrm{2}}$, a mixed valence Sn(II)/Sn(IV) tin nitride, which, due to its metastability relative to metallic Sn, N$_{\mathrm{2}}$, and Sn$_{\mathrm{3}}$N$_{\mathrm{4,}}$ remained elusive until recently [1]. This metastability presents a challenge for computational structure prediction, as common ground state search strategies are guided by energy minimization, which will eventually lead to a phase-separated configuration (Sn$+$N$_{\mathrm{2}})$ instead of the desired Sn$_{\mathrm{2}}$N$_{\mathrm{2}}$ compound. Initial structure sampling has identified a number of candidate structures [1], but did not lead to an unequivocal assignment. We present the results of a new hybrid structure sampling approach predicting a bilayer structure with the possibility of polytypism. [1] C.M. Caskey \textit{et al.}, J. Chem. Phys. 144, 144201 (2016).   

Learning phase transitions by confusion

Classifying phases of matter is a central problem in physics. For quantum mechanical systems, this task can be daunting owing to the exponentially large Hilbert space. Thanks to the available computing power and access to ever larger data sets, classification problems are now routinely solved using machine learning techniques. Here, we propose to use a neural network based approach to find transitions depending on the performance of the neural network after training it with deliberately incorrectly labelled data. We demonstrate the success of this method on the topological phase transition in the Kitaev chain, the thermal phase transition in the classical Ising model, and the many-body-localization transition in a disordered quantum spin chain. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to a generic tool to identify unexplored transitions.   

Projected Regression Methods for Inverting Fredholm Integrals: Formalism and Application to Analytical Continuation

We present a machine learning-based statistical regression approach to the inversion of Fredholm integrals of the first kind by studying an important example for the quantum materials community, the analytical continuation problem of quantum many-body physics. It involves reconstructing the frequency dependence of physical excitation spectra from data obtained at specific points in the complex frequency plane. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned and yields robust error metrics. The stability of the forward problem permits the construction of a large database of input-output pairs. Machine learning methods applied to this database generate approximate solutions which are projected onto the subspace of functions satisfying relevant constraints. We show that for low input noise the method performs as well or better than Maximum Entropy (MaxEnt) under standard error metrics, and is substantially more robust to noise. We expect the methodology to be similarly effective for any problem involving a formally ill-conditioned inversion, provided that the forward problem can be efficiently solved.   

Ferret: an open-source code for simulating thermodynamical evolution and phase transformations in complex materials systems at mesoscale

Ferret is an open-source real-space finite-element-method (FEM) based code for simulating behavior of materials systems with coupled physical properties at mesoscale. It is built on MOOSE, Multiphysics Object Oriented Simulation Environment, and is being developed by the UConn-ANL collaboration. Here we provide an overview of computational approach utilized by the code, as well as its technical features and the associated software within our computational tool chain. We also highlight a variety of code application examples that are being pursued in collaboration with a number of different experimental groups. These applications include (a) evaluations of size- and microstructure-dependent elastic and optical properties of core-shell nanoparticles, including Zn/ZnO and ZnO/TiO$_2$ core/shell material combinations; (b) modeling of the influence of shape, size and elastic distortions of monolithic ZnO and Zn/ZnO core/shell nanowires on their optical properties; (c) studies of the properties and domain-wall dynamics in perovskite-ferroelectric films, nanowires and nanoridges, and (d) investigation of topological phases and size effects in ferroelectric nanoparticles embedded in a dielectic matrix.