Prediction of Low-Thermal-Conductivity Compounds with First-Principles Anharmonic Lattice-Dynamics Calculations and Bayesian Optimization

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

GFN-xTB-Based Computations Provide Comprehensive Insights into Emulsion Radiation-Induced Graft Polymerization

In this article, a deep insight into emulsion radiation-induced graft polymerization (RIGP) was obtained by computing explicit solvation free energies, conformational entropy, monomer radius and dipole moments with the state-of-the-art Conformer-Rotamer Ensemble Sampling Tool (CREST) package primarily at semiempirical GFN-xTB level. By leveraging the robustness of the CREST package, above parameters provided dynamic nature of methacrylate monomers with the consideration of realistic emulsion conditions. With the chemical and physical importance of the above results, CREST-determined explanatory variables sufficiently led to the building of the prediction models for the RIGP of methacrylate monomers. The machine learning model building resulted in effective reactivity predictions and unveiled important factors for the radiation-induced graft polymerization in a chemically interpretable fashion.

Inferring energy-composition relationships with Bayesian optimization enhances exploration of inorganic materials

Computational exploration of the compositional spaces of materials can provide guidance for synthetic research and thus accelerate the discovery of novel materials. Most approaches employ high-throughput sampling and focus on reducing the time for energy evaluation for individual compositions, often at the cost of accuracy. Here, we present an alternative approach focusing on effective sampling of the compositional space. The learning algorithm PhaseBO optimizes the stoichiometry of the potential target material while improving the probability of and accelerating its discovery without compromising the accuracy of energy evaluation.

High-Throughput Strategies in the Discovery of Thermoelectric Materials

Searching for new high-performance thermoelectric (TE) materials that are economical and environmentally friendly is an urgent task for TE society, but the advancements are greatly limited by the time-consuming and high cost of the traditional trial-and-error method. The significant progress achieved in the computing hardware, efficient computing methods, advance artificial intelligence algorithms, and rapidly growing material data have brought a paradigm shift in the investigation of TE materials. Many electrical and thermal performance descriptors are proposed and efficient high-throughput (HTP) calculation methods are developed with the purpose to quickly screen new potential TE materials from the material databases. Some HTP experiment methods are also developed which can increase the density of information obtained in a single experiment with less time and lower cost. In addition, machine learning (ML) methods are also introduced in thermoelectrics. In this review, the HTP strategies in the discovery of TE materials are systematically summarized. The applications of performance descriptor, HTP calculation, HTP experiment, and ML in the discovery of new TE materials are reviewed. In addition, the challenges and possible directions in future research are also discussed.

High-Throughput Computational Design of 2D Ternary Chalcogenides for Sustainable Energy

Two-dimensional materials are considered to be promising for next-generation electronic and energy devices. However, the limited availability of 2D materials hinders their applications. Herein, we employed high-throughput computation to discover new 2D materials by cleaving the bulk and to investigate their electronic, thermoelectric, and optoelectronic properties. Using our database containing 810 structures of chalcogenides ABX3 (A or B = Al, Ga, In, Si, Ge, Sn, P, As, Sb, and Bi; X = S, Se, and Te), we identified 204 new 2D compounds promising for experimental preparation according to the exfoliation energy. Notably, 96 of them are more easily exfoliated than graphene, 52 compounds show higher Seebeck coefficients than Bi2Te3 at 300 K, and 20 compounds have power factors beyond 2 × 10-3 Wm-1 K-2 at 900 K. Also, 6 new compounds exhibit high theoretical photovoltaic efficiency exceeding 30%. Our findings expand the 2D materials family and provide new 2D compounds for sustainable thermoelectric and optoelectronic energy applications.

Exploring Metal Nanocluster Catalysts for Ammonia Synthesis Using Informatics Methods: A Concerted Effort of Bayesian Optimization, Swarm Intelligence, and First-Principles Computation

This paper details the use of computational and informatics methods to design metal nanocluster catalysts for efficient ammonia synthesis. Three main problems are tackled: defining a measure of catalytic activity, choosing the best candidate from a large number of possibilities, and identifying the thermodynamically stable cluster catalyst structure. First-principles calculations, Bayesian optimization, and particle swarm optimization are used to obtain a Ti8 nanocluster as a catalyst candidate. The N2 adsorption structure on Ti8 indicates substantial activation of the N2 molecule, while the NH3 adsorption structure suggests that NH3 is likely to undergo easy desorption. The study also reveals several cluster catalyst candidates that break the general trade-off that surfaces that strongly adsorb reactants also strongly adsorb products.

Gaussian approximation potentials for accurate thermal properties of two-dimensional materials

Two-dimensional materials (2DMs) continue to attract a lot of attention, particularly for their extreme flexibility and superior thermal properties. Molecular dynamics simulations are among the most powerful methods for computing these properties, but their reliability depends on the accuracy of interatomic interactions. While first principles approaches provide the most accurate description of interatomic forces, they are computationally expensive. In contrast, classical force fields are computationally efficient, but have limited accuracy in interatomic force description. Machine learning interatomic potentials, such as Gaussian Approximation Potentials, trained on density functional theory (DFT) calculations offer a compromise by providing both accurate estimation and computational efficiency. In this work, we present a systematic procedure to develop Gaussian approximation potentials for selected 2DMs, graphene, buckled silicene, and h-XN (X = B, Al, and Ga, as binary compounds) structures. We validate our approach through calculations that require various levels of accuracy in interatomic interactions. The calculated phonon dispersion curves and lattice thermal conductivity, obtained through harmonic and anharmonic force constants (including fourth order) are in excellent agreement with DFT results. HIPHIVE calculations, in which the generated GAP potentials were used to compute higher-order force constants instead of DFT, demonstrated the first-principles level accuracy of the potentials for interatomic force description. Molecular dynamics simulations based on phonon density of states calculations, which agree closely with DFT-based calculations, also show the success of the generated potentials in high-temperature simulations.

A Critical Review of Machine Learning Techniques on Thermoelectric Materials

Thermoelectric (TE) materials can directly convert heat to electricity and vice versa and have broad application potential for solid-state power generation and refrigeration. Over the past few decades, efforts have been made to develop new TE materials with high performance. However, traditional experiments and simulations are expensive and time-consuming, limiting the development of new materials. Machine learning (ML) has been increasingly applied to study TE materials in recent years. This paper reviews the recent progress in ML-based TE material research. The application of ML in predicting and optimizing the properties of TE materials, including electrical and thermal transport properties and optimization of functional materials with targeted TE properties, is reviewed. Finally, future research directions are discussed.

Transition-Metal Interlink Neural Network: Machine Learning of 2D Metal-Organic Frameworks with High Magnetic Anisotropy

Two-dimensional (2D) metal-organic framework (MOF) materials with large perpendicular magnetic anisotropy energy (MAE) are important candidates for high-density magnetic storage. The MAE-targeted high-throughput screening of 2D MOFs is currently limited by the time-consuming electronic structure calculations. In this study, a machine learning model, namely, transition-metal interlink neural network (TMINN) based on a database with 1440 2D MOF materials is developed to quickly and accurately predict MAE. The well-trained TMINN model for MAE successfully captures the general correlation between the geometrical configurations and the MAEs. We explore the MAEs of 2583 other 2D MOFs using our trained TMINN model. From these two databases, we obtain 11 unreported 2D ferromagnetic MOFs with MAEs over 35 meV/atom, which are further demonstrated by the high-level density functional theory calculations. Such results show good performance of the extrapolation predictions of TMINN. We also propose some simple design rules to acquire 2D MOFs with large MAEs by building a Pearson correlation coefficient map between various geometrical descriptors and MAE. Our developed TMINN model provides a powerful tool for high-throughput screening and intentional design of 2D magnetic MOFs with large MAE.

Phonon anharmonicity in binary chalcogenides for efficient energy harvesting

Thermoelectric (TE) materials have received much attention due to their ability to harvest waste heat energy. TE materials must exhibit a low thermal conductivity (κ) and a high power factor (PF) for efficient conversion. Both factors define the figure of merit (ZT) of the TE material, which can be increased by suppressing κ without degrading the PF. Recently, binary chalcogenides such as SnSe, GeTe, and PbTe have emerged as attractive candidates for thermoelectric energy generation at moderately high temperatures. These materials possess simple crystal structures with low κ in their pristine forms, which can be further lowered through doping and other approaches. Here, we review the recent advances in the temperature-dependent behavior of phonons and their influence on the thermal transport properties of chalcogenide-based TE materials. Because phonon anharmonicity is one of the fundamental contributing factors for low thermal conductivity in SnSe, Sb-doped GeTe, and related chalcogenides, we discuss complementary experimental approaches such as temperature-dependent Raman spectroscopy, inelastic neutron scattering, and calorimetry to measure anharmonicity. We further show how data gathered using multiple techniques helps us understand and engineer better TE materials. Finally, we discuss the rise of machine learning-aided efforts to discover, design, and synthesize TE materials of the future.

A rapid feature selection method for catalyst design: Iterative Bayesian additive regression trees (iBART)

Feature selection (FS) methods often are used to develop data-driven descriptors (i.e., features) for rapidly predicting the functional properties of a physical or chemical system based on its composition and structure. FS algorithms identify descriptors from a candidate pool (i.e., feature space) built by feature engineering (FE) steps that construct complex features from the system's fundamental physical properties. Recursive FE, which involves repeated FE operations on the feature space, is necessary to build features with sufficient complexity to capture the physical behavior of a system. However, this approach creates a highly correlated feature space that contains millions or billions of candidate features. Such feature spaces are computationally demanding to process using traditional FS approaches that often struggle with strong collinearity. Herein, we address this shortcoming by developing a new method that interleaves the FE and FS steps to progressively build and select powerful descriptors with reduced computational demand. We call this method iterative Bayesian additive regression trees (iBART), as it iterates between FE with unary/binary operators and FS with Bayesian additive regression trees (BART). The capabilities of iBART are illustrated by extracting descriptors for predicting metal-support interactions in catalysis, which we compare to those predicted in our previous work using other state-of-the-art FS methods (i.e., least absolute shrinkage and selection operator + l0, sure independence screening and sparsifying operator, and Bayesian FS). iBART matches the performance of these methods yet uses a fraction of the computational resources because it generates a maximum feature space of size O(102), as opposed to O(106) generated by one-shot FE/FS methods.

Crystal structure prediction by combining graph network and optimization algorithm

Crystal structure prediction is a long-standing challenge in condensed matter and chemical science. Here we report a machine-learning approach for crystal structure prediction, in which a graph network (GN) is employed to establish a correlation model between the crystal structure and formation enthalpies at the given database, and an optimization algorithm (OA) is used to accelerate the search for crystal structure with lowest formation enthalpy. The framework of the utilized approach (a database + a GN model + an optimization algorithm) is flexible. We implemented two benchmark databases, i.e., the open quantum materials database (OQMD) and Matbench (MatB), and three OAs, i.e., random searching (RAS), particle-swarm optimization (PSO) and Bayesian optimization (BO), that can predict crystal structures at a given number of atoms in a periodic cell. The comparative studies show that the GN model trained on MatB combined with BO, i.e., GN(MatB)-BO, exhibit the best performance for predicting crystal structures of 29 typical compounds with a computational cost three orders of magnitude less than that required for conventional approaches screening structures through density functional theory calculation. The flexible framework in combination with a materials database, a graph network, and an optimization algorithm may open new avenues for data-driven crystal structural predictions.

Agents for sequential learning using multiple-fidelity data

Sequential learning for materials discovery is a paradigm where a computational agent solicits new data to simultaneously update a model in service of exploration (finding the largest number of materials that meet some criteria) or exploitation (finding materials with an ideal figure of merit). In real-world discovery campaigns, new data acquisition may be costly and an optimal strategy may involve using and acquiring data with different levels of fidelity, such as first-principles calculation to supplement an experiment. In this work, we introduce agents which can operate on multiple data fidelities, and benchmark their performance on an emulated discovery campaign to find materials with desired band gap values. The fidelities of data come from the results of DFT calculations as low fidelity and experimental results as high fidelity. We demonstrate performance gains of agents which incorporate multi-fidelity data in two contexts: either using a large body of low fidelity data as a prior knowledge base or acquiring low fidelity data in-tandem with experimental data. This advance provides a tool that enables materials scientists to test various acquisition and model hyperparameters to maximize the discovery rate of their own multi-fidelity sequential learning campaigns for materials discovery. This may also serve as a reference point for those who are interested in practical strategies that can be used when multiple data sources are available for active or sequential learning campaigns.

Study of crystal properties based on attention mechanism and crystal graph convolutional neural network

The prediction of crystal properties has always been limited by huge computational costs. In recent years, the rise of machine learning methods has gradually made it possible to study crystal properties on a large scale. We propose an attention mechanism-based crystal graph convolutional neural network, which builds a machine learning model by inputting crystallographic information files and target properties. In our research, the attention mechanism is introduced in the crystal graph convolutional neural network (CGCNN) to learn the local chemical environment, and node normalization is added to reduce the risk of overfitting. We collect structural information and calculation data of about 36 000 crystals and examine the prediction performance of the models for the formation energy, total energy, bandgap, and Fermi energy of crystals in our research. Compared with the CGCNN, it is found that the accuracy (ACCU) of the predicted properties can be further improved to varying degrees by the introduction of the attention mechanism. Moreover, the total magnetization and bandgap can be classified under the same neural network framework. The classification ACCU of wide bandgap semiconductor crystals with a bandgap threshold of 2.3 eV reaches 93.2%, and the classification ACCU of crystals with a total magnetization threshold of 0.5 μ_Breaches 88.8%. The work is helpful to realize large-scale prediction and classification of crystal properties, accelerating the discovery of new functional crystal materials.

Data-Driven Methods for Accelerating Polymer Design

Optimal design of polymers is a challenging task due to their enormous chemical and configurational space. Recent advances in computations, machine learning, and increasing trends in data and software availability can potentially address this problem and accelerate the molecular-scale design of polymers. Here, the central problem of polymer design is reviewed, and the general ideas of data-driven methods and their working principles in the context of polymer design are discussed. This Review provides a historical perspective and a summary of current trends and outlines future scopes of data-driven methods for polymer research. A few representative case studies on the use of such data-driven methods for discovering new polymers with exceptional properties are presented. Moreover, attempts are made to highlight how data-driven strategies aid in establishing new correlations and advancing the fundamental understanding of polymers. This Review posits that the combination of machine learning, rapid computational characterization of polymers, and availability of large open-sourced homogeneous data will transform polymer research and development over the coming decades. It is hoped that this Review will serve as a useful reference to researchers who wish to develop and deploy data-driven methods for polymer research and education.

Descriptors of intrinsic hydrodynamic thermal transport: screening a phonon database in a machine learning approach

Machine learning techniques are used to explore the intrinsic origins of the hydrodynamic thermal transport and to find new materials interesting for science and engineering. The hydrodynamic thermal transport is governed intrinsically by the hydrodynamic scale and the thermal conductivity. The correlations between these intrinsic properties and harmonic and anharmonic properties, and a large number of compositional (290) and structural (1224) descriptors of 131 crystal compound materials are obtained, revealing some of the key descriptors that determines the magnitude of the intrinsic hydrodynamic effects, most of them related with the phonon relaxation times. Then, a trained black-box model is applied to screen more than 5000 materials. The results identify materials with potential technological applications. Understanding the properties correlated to hydrodynamic thermal transport can help to find new thermoelectric materials and on the design of new materials to ease the heat dissipation in electronic devices.

Fe-Al-Si Thermoelectric (FAST) Materials and Modules: Diffusion Couple and Machine-Learning-Assisted Materials Development

To lower the introduction and maintenance costs of autonomous power supplies for driving Internet-of-things (IoT) devices, we have developed low-cost Fe-Al-Si-based thermoelectric (FAST) materials and power generation modules. Our development approach combines computational science, experiments, mapping measurements, and machine learning (ML). FAST materials have a good balance of mechanical properties and excellent chemical stability, superior to that of conventional Bi-Te-based materials. However, it remains challenging to enhance the power factor (PF) and lower the thermal conductivity of FAST materials to develop reliable power generation devices. This forum paper describes the current status of materials development based on experiments and ML with limited data, together with power generation module fabrication related to FAST materials with a view to commercialization. Combining bulk combinatorial methods with diffusion couple and mapping measurements could accelerate the search to enhance PF for FAST materials. We report that ML prediction is a powerful tool for finding unexpected off-stoichiometric compositions of the Fe-Al-Si system and dopant concentrations of a fourth element to enhance the PF, i.e., Co substitution for Fe atoms in FAST materials.

Cross-property deep transfer learning framework for enhanced predictive analytics on small materials data

Artificial intelligence (AI) and machine learning (ML) have been increasingly used in materials science to build predictive models and accelerate discovery. For selected properties, availability of large databases has also facilitated application of deep learning (DL) and transfer learning (TL). However, unavailability of large datasets for a majority of properties prohibits widespread application of DL/TL. We present a cross-property deep-transfer-learning framework that leverages models trained on large datasets to build models on small datasets of different properties. We test the proposed framework on 39 computational and two experimental datasets and find that the TL models with only elemental fractions as input outperform ML/DL models trained from scratch even when they are allowed to use physical attributes as input, for 27/39 (≈ 69%) computational and both the experimental datasets. We believe that the proposed framework can be widely useful to tackle the small data challenge in applying AI/ML in materials science.

Machine Learning-Assisted Development of Sensitive Electrode Materials for Mixed Potential-Type NO2 Gas Sensors

Yttrium-stabilized zirconia (YSZ)-based mixed potential-type NO_x sensors have broad application prospects in automotive exhaust gas detection. Great efforts continue to be made in developing high-performance sensitive electrode materials for mixed potential-type NO₂ gas sensors. However, only five kinds of new sensing electrode materials have been developed for this type of gas sensor in the last 3 years. In this work, four different tree-based machine learning models were trained to find potentially sensitive electrode materials for NO₂ detection. More than 400 materials were selected from 8000 materials by the above machine learning models. To further verify the reliability of the model, 13 of these materials containing unexploited elements were selected as sensitive electrode materials for making sensors and testing their gas-sensing performances. The experimental results showed that all 13 materials exhibited good gas-sensing performance for NO₂. More interestingly, an electrode material BPO₄, which does not contain any metal elements, was also screened out and showed good sensing properties to NO₂. In a short period of time, 13 new sensitive electrode materials for NO₂ detection were targeted and screened, which was difficult to achieve by a trial-and-error procedure.

Machine Learning to Predict Quasicrystals from Chemical Compositions

Quasicrystals have emerged as the third class of solid-state materials, distinguished from periodic crystals and amorphous solids, which have long-range order without periodicity exhibiting rotational symmetries that are disallowed for periodic crystals in most cases. To date, more than one hundred stable quasicrystals have been reported, leading to the discovery of many new and exciting phenomena. However, the pace of the discovery of new quasicrystals has lowered in recent years, largely owing to the lack of clear guiding principles for the synthesis of new quasicrystals. Here, it is shown that the discovery of new quasicrystals can be accelerated with a simple machine-learning workflow. With a list of the chemical compositions of known stable quasicrystals, approximant crystals, and ordinary crystals, a prediction model is trained to solve the three-class classification task and its predictability compared to the observed phase diagrams of ternary aluminum systems is evaluated. The validation experiments strongly support the superior predictive power of machine learning, with the overall prediction accuracy of the phase prediction task reaching ≈0.728. Furthermore, analyzing the input-output relationships black-boxed into the model, nontrivial empirical equations interpretable by humans that describe conditions necessary for stable quasicrystal formation are identified.

Good Solid-State Electrolytes Have Low, Glass-Like Thermal Conductivity

Thermal management in Li-ion batteries is critical for their safety, reliability, and performance. Understanding the thermal conductivity of the battery materials is crucial for controlling the temperature and temperature distribution in batteries. This work provides systemic quantitative measurements of the thermal conductivity of three important classes of solid electrolytes (SEs) over the temperature range 150 < T < 350 K. Studies include the oxides Li_1.5 Al_0.5 Ge_1.5 (PO₄ )₃ and Li_6.4 La₃ Zr_1.4 Ta_0.6 O₁₂ , sulfides Li₂ S-P₂ S₅ , Li₆ PS₅ Cl, and Na₃ PS₄ , and halides Li₃ InCl₆ and Li₃ YCl₆ . Thermal conductivities of sulfide and halide SEs are in the range 0.45-0.70 W m^-1  K^-1 ; thermal conductivities of Li_6.4 La₃ Zr_1.4 Ta_0.6 O₁₂ and Li_1.5 Al_0.5 Ge_1.5 (PO₄ )₃ are 1.4 and 2.2 W m^-1  K^-1 , respectively. For most of the SEs studied in this work, the thermal conductivity increases with increasing temperature, that is, the thermal conductivity has a glass-like temperature dependence. The measured room-temperature thermal conductivities agree well with the calculated minimum thermal conductivities indicating that the phonon mean-free-paths in these SEs are close to an atomic spacing. The low, glass-like thermal conductivity of the SEs investigated is attributed to the combination of their complex crystal structures and the atomic-scale disorder induced by the materials processing methods that are typically needed to produce high ionic conductivities.

Bayesian optimization for goal-oriented multi-objective inverse material design

Bayesian optimization (BO) can accelerate material design requiring time-consuming experiments. However, although most material designs require tuning of multiple properties, the efficiency of multi-objective (MO) BO in time-consuming experimental material design remains unclear, due to the complexity of handling multiple objectives. This study introduces MO BO method that efficiently achieves predefined goals and shows that by focusing on achieving the goals, BO can efficiently accelerate realistic MO design problems with small efforts. Benchmarks showed that the proposed BO method dramatically reduced the number of experiments needed to achieve goals relative to a baseline method. Virtual MO inverse design experiments with realistic material design problems were also performed, during which the proposed method could achieve goals within only around ten experiments in average and showed over 1000-fold acceleration relative to the random sampling for the most difficult case. The introduction of goal-oriented BO will precede real-world application of BO.

Decomposition Factor Analysis Based on Virtual Experiments throughout Bayesian Optimization for Compost-Degradable Polymers

Bio-based polymers have been considered as an alternative to oil-based materials for their “carbon-neutral” environmentally degrative features. However, degradation is a complex system in which environmental factors and preparation conditions are involved, and the relationship between degradation and these factors/conditions has not yet been clarified. Moreover, an efficient system that addresses multiple degradation factors has not been developed for practical use. Thus, we constructed a decomposition degree predictive model to explore degradation factors based on analytical data and experimental conditions. The predictive model was constructed by machine learning using a dataset. The objective variable was the molecular weight, and the explanatory variables were the moisture content in a compost environment, degradation period, degree of crystallinity pre-experiment, and features of solid-state nuclear magnetic resonance spectra. The good accuracy of this predictive model was confirmed by statistical variables. The moisture content in the compost environment was a critical factor for considering initial degradation; specific scores revealed the contribution of degradation factors. Furthermore, the optimum decomposition degree, various analytical values, and experimental conditions were predictable when this predictive model was combined with Bayesian optimization. Information obtained from virtual experiments is expected to promote the material design and development of bio-based plastics.

Black-Box Optimization for Automated Discovery

In chemistry and materials science, researchers and engineers discover, design, and optimize chemical compounds or materials with their professional knowledge and techniques. At the highest level of abstraction, this process is formulated as black-box optimization. For instance, the trial-and-error process of synthesizing various molecules for better material properties can be regarded as optimizing a black-box function describing the relation between a chemical formula and its properties. Various black-box optimization algorithms have been developed in the machine learning and statistics communities. Recently, a number of researchers have reported successful applications of such algorithms to chemistry. They include the design of photofunctional molecules and medical drugs, optimization of thermal emission materials and high Li-ion conductive solid electrolytes, and discovery of a new phase in inorganic thin films for solar cells.There are a wide variety of algorithms available for black-box optimization, such as Bayesian optimization, reinforcement learning, and active learning. Practitioners need to select an appropriate algorithm or, in some cases, develop novel algorithms to meet their demands. It is also necessary to determine how to best combine machine learning techniques with quantum mechanics- and molecular mechanics-based simulations, and experiments. In this Account, we give an overview of recent studies regarding automated discovery, design, and optimization based on black-box optimization. The Account covers the following algorithms: Bayesian optimization to optimize the chemical or physical properties, an optimization method using a quantum annealer, best-arm identification, gray-box optimization, and reinforcement learning. In addition, we introduce active learning and boundless objective-free exploration, which may not fall into the category of black-box optimization.Data quality and quantity are key for the success of these automated discovery techniques. As laboratory automation and robotics are put forward, automated discovery algorithms would be able to match human performance at least in some domains in the near future.

Topological representations of crystalline compounds for the machine-learning prediction of materials properties

Accurate theoretical predictions of desired properties of materials play an important role in materials research and development. Machine learning (ML) can accelerate the materials design by building a model from input data. For complex datasets, such as those of crystalline compounds, a vital issue is how to construct low-dimensional representations for input crystal structures with chemical insights. In this work, we introduce an algebraic topology-based method, called atom-specific persistent homology (ASPH), as a unique representation of crystal structures. The ASPH can capture both pairwise and many-body interactions and reveal the topology-property relationship of a group of atoms at various scales. Combined with composition-based attributes, ASPH-based ML model provides a highly accurate prediction of the formation energy calculated by density functional theory (DFT). After training with more than 30,000 different structure types and compositions, our model achieves a mean absolute error of 61 meV/atom in cross-validation, which outperforms previous work such as Voronoi tessellations and Coulomb matrix method using the same ML algorithm and datasets. Our results indicate that the proposed topology-based method provides a powerful computational tool for predicting materials properties compared to previous works.

Prediction of Bi2Te3-Sb2Te3 Interfacial Conductance and Superlattice Thermal Conductivity Using Molecular Dynamics Simulations

Bismuth telluride (Bi₂Te₃) and its alloys with antimony telluride (Sb₂Te₃) have long been considered to be the best room-temperature bulk thermoelectric (TE) materials. In recent decades, proof-of-concept demonstrations on Bi₂Te₃-Sb₂Te₃ nanostructures have shown high TE performance due to reduction in lattice thermal conductivities. Particularly, ultra-low thermal conductivities have been observed in Bi₂Te₃-Sb₂Te₃ 1D superlattices, leading to thermoelectric figures of merit (ZT) as high as 2.4. In contrast, very few computational studies have been performed to provide insight into the phonon transport across these nanostructures. In this work, we use non-equilibrium molecular dynamics simulations with previously developed force fields to simulate thermal transport across Bi₂Te₃-Sb₂Te₃ interfaces and superlattices. We first calculate the thermal conductance associated with a Bi₂Te₃-Sb₂Te₃ interface across a temperature range of 200-400 K. The values are also compared with thermal conductances calculated by a modified Landauer transport formalism using phonon transmission coefficients obtained from the diffuse mismatch model. Our results show that inelastic scattering processes contribute to an increase in interfacial thermal conductance at higher temperatures. Finally, we calculate the thermal conductivities of Bi₂Te₃-Sb₂Te₃ superlattices with varying period lengths from 2 to 18 nm. A minimum thermal conductivity of 0.27 W/mK is observed at a period length of 4 nm, which is attributed to the competition between incoherent and coherent phonon transport regimes. In comparison with previous experimental measurements in the literature, our results show good agreement with respect to the range of thermal conductivity values and the period length corresponding to the minimum superlattice thermal conductivity.

Why thermal conductivity of CaO is lower than that of CaS: a study from the perspective of phonon splitting of optical mode

Generally speaking, for materials with the same structure, the thermal conductivity is higher for lighter atomic masses. However, we found that the thermal conductivity of CaO is lower than that of CaS, despite the lighter atomic mass of O than S. To uncover the underlying physical mechanisms, the thermal conductivity of CaM (M = O, S, Se, Te) and the corresponding response to strain is investigated by performing first-principles calculations along with the phonon Boltzmann transport equation. For unstrained system, the order of thermal conductivity is CaS > CaO > CaSe > CaTe. This order remains unchanged in the strain range of -2% to 5%. When the compressive strain is larger than 2%, the thermal conductivity of CaO surpasses that of CaS and becomes the highest thermal conductivity material among the four compounds. By analyzing the mode-dependent phonon properties, the phonon lifetime is found to be dominant over other influential factors and leads to the disparate response of thermal conductivity under strain. Moreover, the changing trend of three-phonon scattering phase space is consistent with that of phonon lifetime, which is directly correlated to the phonon frequency gap induced by the LO-TO splitting. The variation of Born effective charge is found to be opposite for CaM. The Born effective charge of CaO decreases with tensile strain increasing, demonstrating stronger charge delocalization and lower ionicity, while the Born effective charges of CaS, CaSe, and CaTe show a dramatic increase. Such variation indicates that the bonding nature can be effectively tuned by external strain, thus affecting the phonon anharmonic properties and thermal conductivity. The difference of bonding nature is further confirmed by the band structure. Our results show that the bonding nature of CaM can be modulated by external strain and leads to disparate strain dependent thermal conductivity.

Geometrical design of a crystal growth system guided by a machine learning algorithm

This study proposes a new high-speed method for designing crystal growth systems. It is capable of optimizing large numbers of parameters simultaneously which is difficult for traditional experimental and computational techniques.

First-principles predictions of low lattice thermal conductivity and high thermoelectric performance of AZnSb (A = Rb, Cs)

Here, two compounds, AZnSb (A = Rb, Cs), have been predicted to be potential materials for thermoelectric device applications at high temperatures by using first-principles calculations based on density functional theory (DFT), density functional perturbation theory (DFPT), and Boltzmann transport theory. The layered structure, and presence of heavier elements Rb/Cs and Sb induce high anharmonicity (larger values of mode Grüneisen parameter), low Debye temperature, and intense phonon scattering. Thus, these compounds possess intrinsically low lattice thermal conductivity (κ_l), ∼0.5 W m⁻¹ K⁻¹ on average at 900 K. Highly non-parabolic bands and relatively wide bandgap (∼1.37 and 1.1 eV for RbZnSb and CsZnSb, respectively, by mBJ potential including spin–orbit coupling effect) induce large Seebeck coefficient while highly dispersive and two-fold degenerate bands induce high electrical conductivity. Large power factor and low values of κ_l lead to a high average thermoelectric figure of merit (ZT) of RbZnSb and CsZnSb, reaching 1.22 and 1.1 and 0.87 and 1.14 at 900 K for p-and n-type carriers, respectively.

The layered structure, and presence of heavier elements Rb/Cs and Sb induce high anharmonicity, low Debye temperature, intense phonon scattering, and hence, low lattice thermal conductivity.

Lattice Thermal Conductivity Prediction Using Symbolic Regression and Machine Learning

Prediction models of lattice thermal conductivity (κ_L) have wide applications in the discovery of thermoelectrics, thermal barrier coatings, and thermal management of semiconductors. However, κ_L is notoriously difficult to predict. Although classic models such as the Debye-Callaway model and the Slack model have been used to approximate the κ_L of inorganic compounds, their accuracy is far from being satisfactory. Herein we propose a genetic programming-based symbolic regression (SR) approach for finding analytical κ_L models and compare them with multilayer perceptron neural networks and random forest regression models using a hybrid cross-validation (CV) approach including both K-fold CV and holdout validation. Four formulae have been discovered by our SR approach that outperform the Slack formula as evaluated on our dataset. Through the analysis of our models' performance and the formulae generated, we found that the trained formulae successfully reproduce the correct physical law that governs the lattice thermal conductivity of materials. We also systematically show that currently extrapolative prediction over datasets with different distributions as the training set remains to be a big challenge for both SR and machine learning-based prediction models.

Identifying Optimal Strain in Bismuth Telluride Thermoelectric Film by Combinatorial Gradient Thermal Annealing and Machine Learning

The thermoelectric properties of bismuth telluride thin film (BTTF) was tuned by inducing internal strain through a combination of combinatorial gradient thermal annealing (COGTAN) and machine learning. BTTFs were synthesized via magnetron sputter coating and then treated by COGTAN. The crystal structure and thermoelectric properties, namely Seebeck coefficient and thermal conductivity, of the treated samples were analyzed via micropoint X-ray diffraction and scanning thermal probe microimaging, respectively. The obtained combinatorial data reveals the correlation between internal strain and the thermoelectric properties. The Seebeck coefficient of BTTF exhibits largest sensitivity, where the value ranges from 7.9 to -108 μV/K. To further explore the possibility to enhance Seebeck coefficient, the combinatorial data were subjected to machine learning. The trained model predicts that optimal strains of 3-4% and 1-2% along the a- and c-axis, respectively, significantly improve Seebeck coefficient. The technique demonstrated herein can be used to predict and enhance the performance of thermoelectric materials by inducing internal strain.

Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal-organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0-300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal-organic crystal are off by up to 100%.

Data-driven studies of magnetic two-dimensional materials

We use a data-driven approach to study the magnetic and thermodynamic properties of van der Waals (vdW) layered materials. We investigate monolayers of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {A}_2\hbox {B}_2\hbox {X}_6$$\end{document}A2B2X6, based on the known material \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Cr}_2\hbox {Ge}_2\hbox {Te}_6$$\end{document}Cr2Ge2Te6, using density functional theory (DFT) calculations and machine learning methods to determine their magnetic properties, such as magnetic order and magnetic moment. We also examine formation energies and use them as a proxy for chemical stability. We show that machine learning tools, combined with DFT calculations, can provide a computationally efficient means to predict properties of such two-dimensional (2D) magnetic materials. Our data analytics approach provides insights into the microscopic origins of magnetic ordering in these systems. For instance, we find that the X site strongly affects the magnetic coupling between neighboring A sites, which drives the magnetic ordering. Our approach opens new ways for rapid discovery of chemically stable vdW materials that exhibit magnetic behavior.

Materials informatics approach to understand aluminum alloys

The relations between the mechanical properties, heat treatment, and compositions of elements in aluminum alloys are extracted by a materials informatics technique. In our strategy, a machine learning model is first trained by a prepared database to predict the properties of materials. The dependence of the predicted properties on explanatory variables, that is, the type of heat treatment and element composition, is searched using a Markov chain Monte Carlo method. From the dependencies, a factor to obtain the desired properties is investigated. Using targets of 5000, 6000, and 7000 series aluminum alloys, we extracted relations that are difficult to find via simple correlation analysis. Our method is also used to design an experimental plan to optimize the materials properties while promoting the understanding of target materials.

Anharmonicity and Ultralow Thermal Conductivity in Lead-Free Halide Double Perovskites

The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs_{2}AgBiBr_{6}, the prototypical compound in this class and show that the lattice dynamics of Cs_{2}AgBiBr_{6} is highly anharmonic, largely in regards to tilting of AgBr_{6} and BiBr_{6} octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs_{2}AgBiBr_{6} yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.

High-Throughput and Autonomous Grazing Incidence X-ray Diffraction Mapping of Organic Combinatorial Thin-Film Library Driven by Machine Learning

High-throughput X-ray diffraction (XRD) is one of the most indispensable techniques to accelerate materials research. However, the conventional XRD analysis with a large beam spot size may not best appropriate in a case for characterizing organic materials thin film libraries, in which various films prepared under different process conditions are integrated on a single substrate. Here, we demonstrate that high-resolution grazing incident XRD mapping analysis is useful for this purpose: A 2-dimensional organic combinatorial thin film library with the composition and growth temperature varied along the two orthogonal axes was successfully analyzed by using synchrotron microbeam X-ray. Moreover, we show that the time-consuming mapping process is accelerated with the aid of a machine learning technique termed as Bayesian optimization based on Gaussian process regression.

Coarse-Grained Diffraction Template Matching Model to Retrieve Multiconformational Models for Biomolecule Structures from Noisy Diffraction Patterns

Biomolecular imaging using X-ray free-electron lasers (XFELs) has been successfully applied to serial femtosecond crystallography. However, the application of single-particle analysis for structure determination using XFELs with 100 nm or smaller biomolecules has two practical problems: the incomplete diffraction data sets for reconstructing 3D assembled structures and the heterogeneous conformational states of samples. A new diffraction template matching method is thus presented here to retrieve a plausible 3D structural model based on single noisy target diffraction patterns, assuming candidate structures. Two concepts are introduced here: prompt candidate diffraction, generated by enhanced sampled coarse-grain (CG) candidate structures, and efficient molecular orientation searching for matching based on Bayesian optimization. A CG model-based diffraction-matching protocol is proposed that achieves a 100-fold speed increase compared to exhaustive diffraction matching using an all-atom model. The conditions that enable multiconformational analysis were also investigated by simulated diffraction data for various conformational states of chromatin and ribosomes. The proposed method can enable multiconformational analysis, with a structural resolution of at least 20 Å for 270-800 Å flexible biomolecules, in experimental single-particle structure analyses that employ XFELs.

Synergy of Binary Substitutions for Improving the Cycle Performance in LiNiO2 Revealed by Ab Initio Materials Informatics

We explore LiNiO₂-based cathode materials with two-element substitutions by an ab initio simulation-based materials informatics (AIMI) approach. According to our previous study, a higher cycle performance strongly correlates with less structural change during the charge-discharge cycles; the latter can be used for evaluating the former. However, if we target the full substitution space, full simulations are infeasible even for all binary combinations. To circumvent such an exhaustive search, we rely on Bayesian optimization. Actually, by searching only 4% of all of the combinations, our AIMI approach discovered two promising combinations, Cr-Mg and Cr-Re, whereas each atom itself never improved the performance. We conclude that the synergy never emerges from a common strategy restricted to combinations of "good" elements that individually improve the performance. In addition, we propose a guideline for the binary substitutions by elucidating the mechanism of the crystal structure change.

Pushing property limits in materials discovery via boundless objective-free exploration

Our developed algorithm, BLOX (BoundLess Objective-free eXploration), successfully found “out-of-trend” molecules potentially useful for photofunctional materials from a drug database.

Materials chemists develop chemical compounds to meet often conflicting demands of industrial applications. This process may not be properly modeled by black-box optimization because the target property is not well defined in some cases. Herein, we propose a new algorithm for automated materials discovery called BoundLess Objective-free eXploration (BLOX) that uses a novel criterion based on kernel-based Stein discrepancy in the property space. Unlike other objective-free exploration methods, a boundary for the materials properties is not needed; hence, BLOX is suitable for open-ended scientific endeavors. We demonstrate the effectiveness of BLOX by finding light-absorbing molecules from a drug database. Our goal is to minimize the number of density functional theory calculations required to discover out-of-trend compounds in the intensity–wavelength property space. Using absorption spectroscopy, we experimentally verified that eight compounds identified as outstanding exhibit the expected optical properties. Our results show that BLOX is useful for chemical repurposing, and we expect this search method to have numerous applications in various scientific disciplines.

Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning

Accompanied with an increase of revealed biomolecular structures owing to advancements in structural biology, the molecular dynamics (MD) approach, especially coarse-grained (CG) MD suitable for macromolecules, is becoming increasingly important for elucidating their dynamics and behavior. In fact, CG-MD simulation has succeeded in qualitatively reproducing numerous biological processes for various biomolecules such as conformational changes and protein folding with reasonable calculation costs. However, CG-MD simulations strongly depend on various parameters, and selecting an appropriate parameter set is necessary to reproduce a particular biological process. Because exhaustive examination of all candidate parameters is inefficient, it is important to identify successful parameters. Furthermore, the successful region, in which the desired process is reproducible, is essential for describing the detailed mechanics of functional processes and environmental sensitivity and robustness. We propose an efficient search method for identifying the successful region by using two machine learning techniques, Bayesian optimization and active learning. We evaluated its performance using F1-ATPase, a biological rotary motor, with CG-MD simulations. We successfully identified the successful region with lower computational costs (12.3% in the best case) without sacrificing accuracy compared to exhaustive search. This method can accelerate not only parameter search but also biological discussion of the detailed mechanics of functional processes and environmental sensitivity based on MD simulation studies.

Electron-phonon scattering and mean free paths in D-carbon

Through first-principles simulations combined with the Wannier function interpolation method, the hot carrier scattering rates of D-carbon are studied. The calculated scattering rates reveal that optical and acoustic phonons dominate the scattering around the valence and the conduction band edges, respectively, while mode-resolved scattering analysis shows that the transverse optical phonons dominate the scattering processes with the energy range 0.2 eV away from the band edges in D-carbon. The relaxation times of holes are significantly longer than those of electrons around the band edges due to the different scattering intensity. In addition, owing to the long lifetimes and the strong dispersion of valence bands, the mean free paths of hot holes are dramatically larger than those of hot electrons.

Benchmarking the acceleration of materials discovery by sequential learning

Sequential learning (SL) strategies, i.e. iteratively updating a machine learning model to guide experiments, have been proposed to significantly accelerate materials discovery and research. Applications on computational datasets and a handful of optimization experiments have demonstrated the promise of SL, motivating a quantitative evaluation of its ability to accelerate materials discovery, specifically in the case of physical experiments. The benchmarking effort in the present work quantifies the performance of SL algorithms with respect to a breadth of research goals: discovery of any "good" material, discovery of all "good" materials, and discovery of a model that accurately predicts the performance of new materials. To benchmark the effectiveness of different machine learning models against these goals, we use datasets in which the performance of all materials in the search space is known from high-throughput synthesis and electrochemistry experiments. Each dataset contains all pseudo-quaternary metal oxide combinations from a set of six elements (chemical space), the performance metric chosen is the electrocatalytic activity (overpotential) for the oxygen evolution reaction (OER). A diverse set of SL schemes is tested on four chemical spaces, each containing 2121 catalysts. The presented work suggests that research can be accelerated by up to a factor of 20 compared to random acquisition in specific scenarios. The results also show that certain choices of SL models are ill-suited for a given research goal resulting in substantial deceleration compared to random acquisition methods. The results provide quantitative guidance on how to tune an SL strategy for a given research goal and demonstrate the need for a new generation of materials-aware SL algorithms to further accelerate materials discovery.