Recent advances in the SISSO method and their implementation in the SISSO++ code.

Accurate and explainable artificial-intelligence (AI) models are promising tools for accelerating the discovery of new materials. Recently, symbolic regression has become an increasingly popular tool for explainable AI because it yields models that are relatively simple analytical descriptions of target properties. Due to its deterministic nature, the sure-independence screening and sparsifying operator (SISSO) method is a particularly promising approach for this application. Here, we describe the new advancements of the SISSO algorithm, as implemented into SISSO++, a C++ code with Python bindings. We introduce a new representation of the mathematical expressions found by SISSO. This is a first step toward introducing "grammar" rules into the feature creation step. Importantly, by introducing a controlled nonlinear optimization to the feature creation step, we expand the range of possible descriptors found by the methodology. Finally, we introduce refinements to the solver algorithms for both regression and classification, which drastically increase the reliability and efficiency of SISSO. For all these improvements to the basic SISSO algorithm, we not only illustrate their potential impact but also fully detail how they operate both mathematically and computationally.

Ab Initio Approach for Thermodynamic Surface Phases with Full Consideration of Anharmonic Effects: The Example of Hydrogen at Si(100).

A reliable description of surfaces structures in a reactive environment is crucial to understand materials' functions. We present a first-principles theory of replica-exchange grand-canonical-ensemble molecular dynamics and apply it to evaluate phase equilibria of surfaces in a reactive gas-phase environment. We identify the different surface phases and locate phase boundaries including triple and critical points. The approach is demonstrated by addressing open questions for the Si(100) surface in contact with a hydrogen atmosphere. In the range from 300 to 1000 K, we find 25 distinct thermodynamically stable surface phases, for which we also provide microscopic descriptions. Most of the identified phases, including few order-disorder phase transitions, have not yet been observed experimentally. Furthermore, we show that the dynamic Si-Si bonds forming and breaking is the driving force behind the phase transition between 3×1 and 2×1 adsorption patterns.

Identifying Outstanding Transition-Metal-Alloy Heterogeneous Catalysts for the Oxygen Reduction and Evolution Reactions via Subgroup Discovery.

In order to estimate the reactivity of a large number of potentially complex heterogeneous catalysts while searching for novel and more efficient materials, physical as well as data-centric models have been developed for a faster evaluation of adsorption energies compared to first-principles calculations. However, global models designed to describe as many materials as possible might overlook the very few compounds that have the appropriate adsorption properties to be suitable for a given catalytic process. Here, the subgroup-discovery (SGD) local artificial-intelligence approach is used to identify the key descriptive parameters and constrains on their values, the so-called SG rules, which particularly describe transition-metal surfaces with outstanding adsorption properties for the oxygen-reduction and -evolution reactions. We start from a data set of 95 oxygen adsorption-energy values evaluated by density-functional-theory calculations for several monometallic surfaces along with 16 atomic, bulk and surface properties as candidate descriptive parameters. From this data set, SGD identifies constraints on the most relevant parameters describing materials and adsorption sites that (i) result in O adsorption energies within the Sabatier-optimal range required for the oxygen-reduction reaction and (ii) present the largest deviations from the linear-scaling relations between O and OH adsorption energies, which limit the catalyst performance in the oxygen-evolution reaction. The SG rules not only reflect the local underlying physicochemical phenomena that result in the desired adsorption properties, but also guide the challenging design of alloy catalysts. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11244-021-01502-4.

Learning Design Rules for Selective Oxidation Catalysts from High-Throughput Experimentation and Artificial Intelligence.

The design of heterogeneous catalysts is challenged by the complexity of materials and processes that govern reactivity and by the fact that the number of good catalysts is very small in comparison to the number of possible materials. Here, we show how the subgroup-discovery (SGD) artificial-intelligence approach can be applied to an experimental plus theoretical data set to identify constraints on key physicochemical parameters, the so-called SG rules, which exclusively describe materials and reaction conditions with outstanding catalytic performance. By using high-throughput experimentation, 120 SiO2-supported catalysts containing ruthenium, tungsten, and phosphorus were synthesized and tested in the catalytic oxidation of propylene. As candidate descriptive parameters, the temperature and 10 parameters related to the composition and chemical nature of the catalyst materials, derived from calculated free-atom properties, were offered. The temperature, the phosphorus content, and the composition-weighted electronegativity are identified as key parameters describing high yields toward the value-added oxygenate products acrolein and acrylic acid. The SG rules not only reflect the underlying processes particularly associated with high performance but also guide the design of more complex catalysts containing up to five elements in their composition.

Artificial-intelligence-driven discovery of catalyst genes with application to CO2 activation on semiconductor oxides.

Catalytic-materials design requires predictive modeling of the interaction between catalyst and reactants. This is challenging due to the complexity and diversity of structure-property relationships across the chemical space. Here, we report a strategy for a rational design of catalytic materials using the artificial intelligence approach (AI) subgroup discovery. We identify catalyst genes (features) that correlate with mechanisms that trigger, facilitate, or hinder the activation of carbon dioxide (CO2) towards a chemical conversion. The AI model is trained on first-principles data for a broad family of oxides. We demonstrate that surfaces of experimentally identified good catalysts consistently exhibit combinations of genes resulting in a strong elongation of a C-O bond. The same combinations of genes also minimize the OCO-angle, the previously proposed indicator of activation, albeit under the constraint that the Sabatier principle is satisfied. Based on these findings, we propose a set of new promising catalyst materials for CO2 conversion.

Robust recognition and exploratory analysis of crystal structures via Bayesian deep learning.

Due to their ability to recognize complex patterns, neural networks can drive a paradigm shift in the analysis of materials science data. Here, we introduce ARISE, a crystal-structure identification method based on Bayesian deep learning. As a major step forward, ARISE is robust to structural noise and can treat more than 100 crystal structures, a number that can be extended on demand. While being trained on ideal structures only, ARISE correctly characterizes strongly perturbed single- and polycrystalline systems, from both synthetic and experimental resources. The probabilistic nature of the Bayesian-deep-learning model allows to obtain principled uncertainty estimates, which are found to be correlated with crystalline order of metallic nanoparticles in electron tomography experiments. Applying unsupervised learning to the internal neural-network representations reveals grain boundaries and (unapparent) structural regions sharing easily interpretable geometrical properties. This work enables the hitherto hindered analysis of noisy atomic structural data from computations or experiments.

Data-driven equation for drug-membrane permeability across drugs and membranes.

Drug efficacy depends on its capacity to permeate across the cell membrane. We consider the prediction of passive drug-membrane permeability coefficients. Beyond the widely recognized correlation with hydrophobicity, we additionally consider the functional relationship between passive permeation and acidity. To discover easily interpretable equations that explain the data well, we use the recently proposed sure-independence screening and sparsifying operator (SISSO), an artificial-intelligence technique that combines symbolic regression with compressed sensing. Our study is based on a large in silico dataset of 0.4 × 106 small molecules extracted from coarse-grained simulations. We rationalize the equation suggested by SISSO via an analysis of the inhomogeneous solubility-diffusion model in several asymptotic acidity regimes. We further extend our analysis to the dependence on lipid-membrane composition. Lipid-tail unsaturation plays a key role but surprisingly contributes stepwise rather than proportionally. Our results are in line with previously observed changes in permeability, suggesting the distinction between liquid-disordered and liquid-ordered permeation. Together, compressed sensing with analytically derived asymptotes establish and validate an accurate, broadly applicable, and interpretable equation for passive permeability across both drug and lipid-tail chemistry.

Materials genes of heterogeneous catalysis from clean experiments and artificial intelligence.

ABSTRACT: The performance in heterogeneous catalysis is an example of a complex materials function, governed by an intricate interplay of several processes (e.g., the different surface chemical reactions, and the dynamic restructuring of the catalyst material at reaction conditions). Modeling the full catalytic progression via first-principles statistical mechanics is impractical, if not impossible. Instead, we show here how a tailored artificial-intelligence approach can be applied, even to a small number of materials, to model catalysis and determine the key descriptive parameters ("materials genes") reflecting the processes that trigger, facilitate, or hinder catalyst performance. We start from a consistent experimental set of "clean data," containing nine vanadium-based oxidation catalysts. These materials were synthesized, fully characterized, and tested according to standardized protocols. By applying the symbolic-regression SISSO approach, we identify correlations between the few most relevant materials properties and their reactivity. This approach highlights the underlying physicochemical processes, and accelerates catalyst design. IMPACT STATEMENT: Artificial intelligence (AI) accepts that there are relationships or correlations that cannot be expressed in terms of a closed mathematical form or an easy-to-do numerical simulation. For the function of materials, for example, catalysis, AI may well capture the behavior better than the theory of the past. However, currently the flexibility of AI comes together with a lack of interpretability, and AI can only predict aspects that were included in the training. The approach proposed and demonstrated in this IMPACT article is interpretable. It combines detailed experimental data (called "clean data") and symbolic regression for the identification of the key descriptive parameters (called "materials genes") that are correlated with the materials function. The approach demonstrated here for the catalytic oxidation of propane will accelerate the discovery of improved or novel materials while also enhancing physical understanding. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1557/s43577-021-00165-6.

Identifying domains of applicability of machine learning models for materials science.

Although machine learning (ML) models promise to substantially accelerate the discovery of novel materials, their performance is often still insufficient to draw reliable conclusions. Improved ML models are therefore actively researched, but their design is currently guided mainly by monitoring the average model test error. This can render different models indistinguishable although their performance differs substantially across materials, or it can make a model appear generally insufficient while it actually works well in specific sub-domains. Here, we present a method, based on subgroup discovery, for detecting domains of applicability (DA) of models within a materials class. The utility of this approach is demonstrated by analyzing three state-of-the-art ML models for predicting the formation energy of transparent conducting oxides. We find that, despite having a mutually indistinguishable and unsatisfactory average error, the models have DAs with distinctive features and notably improved performance.

Viewpoint: Atomic-Scale Design Protocols toward Energy, Electronic, Catalysis, and Sensing Applications.

Nanostructured materials are essential building blocks for the fabrication of new devices for energy harvesting/storage, sensing, catalysis, magnetic, and optoelectronic applications. However, because of the increase of technological needs, it is essential to identify new functional materials and improve the properties of existing ones. The objective of this Viewpoint is to examine the state of the art of atomic-scale simulative and experimental protocols aimed to the design of novel functional nanostructured materials, and to present new perspectives in the relative fields. This is the result of the debates of Symposium I "Atomic-scale design protocols towards energy, electronic, catalysis, and sensing applications", which took place within the 2018 European Materials Research Society fall meeting.

New tolerance factor to predict the stability of perovskite oxides and halides.

Predicting the stability of the perovskite structure remains a long-standing challenge for the discovery of new functional materials for many applications including photovoltaics and electrocatalysts. We developed an accurate, physically interpretable, and one-dimensional tolerance factor, τ, that correctly predicts 92% of compounds as perovskite or nonperovskite for an experimental dataset of 576 ABX 3 materials (X = O2-, F-, Cl-, Br-, I-) using a novel data analytics approach based on SISSO (sure independence screening and sparsifying operator). τ is shown to generalize outside the training set for 1034 experimentally realized single and double perovskites (91% accuracy) and is applied to identify 23,314 new double perovskites (A 2 BB'X 6) ranked by their probability of being stable as perovskite. This work guides experimentalists and theorists toward which perovskites are most likely to be successfully synthesized and demonstrates an approach to descriptor identification that can be extended to arbitrary applications beyond perovskite stability predictions.

(Meta-)stability and Core-Shell Dynamics of Gold Nanoclusters at Finite Temperature.

Gold nanoclusters have been the focus of numerous computational studies, but an atomistic understanding of their structural and dynamical properties at finite temperature is far from satisfactory. To address this deficiency, we investigate gold nanoclusters via ab initio molecular dynamics, in a range of sizes where a core-shell morphology is observed. We analyze their structure and dynamics using state-of-the-art techniques, including unsupervised machine-learning nonlinear dimensionality reduction (sketch-map) for describing the similarities and differences among the range of sampled configurations. In the examined temperature range between 300 and 600 K, we find that whereas the gold nanoclusters exhibit continuous structural rearrangement, they are not amorphous. Instead, they clearly show persistent motifs: a cationic core of 1-5 atoms is loosely bound to a shell which typically displays a substructure resulting from the competition between locally spherical versus planar fragments. Besides illuminating the properties of core-shell gold nanoclusters, the present study proposes a set of useful tools for understanding their nature in operando.

Insightful classification of crystal structures using deep learning.

Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and analytics. Current methods require a user-specified threshold, and are unable to detect average symmetries for defective structures. Here, we propose a machine learning-based approach to automatically classify structures by crystal symmetry. First, we represent crystals by calculating a diffraction image, then construct a deep learning neural network model for classification. Our approach is able to correctly classify a dataset comprising more than 100,000 simulated crystal structures, including heavily defective ones. The internal operations of the neural network are unraveled through attentive response maps, demonstrating that it uses the same landmarks a materials scientist would use, although never explicitly instructed to do so. Our study paves the way for crystal structure recognition of-possibly noisy and incomplete-three-dimensional structural data in big-data materials science.

GAtor: A First-Principles Genetic Algorithm for Molecular Crystal Structure Prediction.

We present the implementation of GAtor, a massively parallel, first-principles genetic algorithm (GA) for molecular crystal structure prediction. GAtor is written in Python and currently interfaces with the FHI-aims code to perform local optimizations and energy evaluations using dispersion-inclusive density functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for molecular crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented in GAtor by using machine learning to cluster the dynamically updated population by structural similarity and then employing a cluster-based fitness function. Evolutionary niching promotes uniform sampling of the potential energy surface by evolving several subpopulations, which helps overcome initial pool biases and selection biases (genetic drift). The various settings offered by GAtor increase the likelihood of locating numerous low-energy minima, including those located in disconnected, hard to reach regions of the potential energy landscape. The best structures generated are re-relaxed and re-ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chemically diverse set of four past blind test targets, characterized by different types of intermolecular interactions. The experimentally observed structures and other low-energy structures are found for all four targets. In particular, for Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z' = 2 structure with P1̅ symmetry and a scaffold packing motif, which has not been reported previously.

Report on the sixth blind test of organic crystal structure prediction methods.

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

Formation of Water Chains on CaO(001): What Drives the 1D Growth?

Formation of partly dissociated water chains is observed on CaO(001) films upon water exposure at 300 K. While morphology and orientation of the 1D assemblies are revealed from scanning tunneling microscopy, their atomic structure is identified with infrared absorption spectroscopy combined with density functional theory calculations. The latter exploit an ab initio genetic algorithm linked to atomistic thermodynamics to determine low-energy H2O configurations on the oxide surface. The development of 1D structures on the C4v symmetric CaO(001) is triggered by symmetry-broken water tetramers and a favorable balance between adsorbate-adsorbate versus adsorbate-surface interactions at the constraint of the CaO lattice parameter.

Big data of materials science: critical role of the descriptor.

Statistical learning of materials properties or functions so far starts with a largely silent, nonchallenged step: the choice of the set of descriptive parameters (termed descriptor). However, when the scientific connection between the descriptor and the actuating mechanisms is unclear, the causality of the learned descriptor-property relation is uncertain. Thus, a trustful prediction of new promising materials, identification of anomalies, and scientific advancement are doubtful. We analyze this issue and define requirements for a suitable descriptor. For a classic example, the energy difference of zinc blende or wurtzite and rocksalt semiconductors, we demonstrate how a meaningful descriptor can be found systematically.

Stability and metastability of clusters in a reactive atmosphere: theoretical evidence for unexpected stoichiometries of MgMOx.

By applying a genetic algorithm and ab initio atomistic thermodynamics, we identify the stable and metastable compositions and structures of MgMOx clusters at realistic temperatures and oxygen pressures. We find that small clusters (M≲5) are in thermodynamic equilibrium when x>M. The nonstoichiometric clusters exhibit peculiar magnetic behavior, suggesting the possibility of tuning magnetic properties by changing environmental pressure and temperature conditions. Furthermore, we show that density-functional theory with a hybrid exchange-correlation functional is needed for predicting accurate phase diagrams of metal-oxide clusters. Neither a (sophisticated) force field nor density-functional theory with (semi)local exchange-correlation functionals is sufficient for even a qualitative prediction.