Understanding the thermal properties of amorphous solids using machine-learning-based interatomic potentials

Machine learning interatomic potential: Bridge the gap between small-scale models and realistic device-scale simulations

Machine learning interatomic potential (MLIP) overcomes the challenges of high computational costs in density-functional theory and the relatively low accuracy in classical large-scale molecular dynamics, facilitating more efficient and precise simulations in materials research and design. In this review, the current state of the four essential stages of MLIP is discussed, including data generation methods, material structure descriptors, six unique machine learning algorithms, and available software. Furthermore, the applications of MLIP in various fields are investigated, notably in phase-change memory materials, structure searching, material properties predicting, and the pre-trained universal models. Eventually, the future perspectives, consisting of standard datasets, transferability, generalization, and trade-off between accuracy and complexity in MLIPs, are reported.

Hyperactive learning for data-driven interatomic potentials

Data-driven interatomic potentials have emerged as a powerful tool for approximating ab initio potential energy surfaces. The most time-consuming step in creating these interatomic potentials is typically the generation of a suitable training database. To aid this process hyperactive learning (HAL), an accelerated active learning scheme, is presented as a method for rapid automated training database assembly. HAL adds a biasing term to a physically motivated sampler (e.g. molecular dynamics) driving atomic structures towards uncertainty in turn generating unseen or valuable training configurations. The proposed HAL framework is used to develop atomic cluster expansion (ACE) interatomic potentials for the AlSi10 alloy and polyethylene glycol (PEG) polymer starting from roughly a dozen initial configurations. The HAL generated ACE potentials are shown to be able to determine macroscopic properties, such as melting temperature and density, with close to experimental accuracy.

Thermal conductivity of glasses: first-principles theory and applications

Predicting the thermal conductivity of glasses from first principles has hitherto been a very complex problem. The established Allen-Feldman and Green-Kubo approaches employ approximations with limited validity-the former neglects anharmonicity, the latter misses the quantum Bose-Einstein statistics of vibrations-and require atomistic models that are very challenging for first-principles methods. Here, we present a protocol to determine from first principles the thermal conductivity κ(T) of glasses above the plateau (i.e., above the temperature-independent region appearing almost without exceptions in the κ(T) of all glasses at cryogenic temperatures). The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques, and accounts comprehensively for the effects of structural disorder, anharmonicity, and Bose-Einstein statistics. We validate this approach in vitreous silica, showing that models containing less than 200 atoms can already reproduce κ(T) in the macroscopic limit. We discuss the effects of anharmonicity and the mechanisms determining the trend of κ(T) at high temperature, reproducing experiments at temperatures where radiative effects remain negligible.

Machine Learning for Harnessing Thermal Energy: From Materials Discovery to System Optimization

Recent advances in machine learning (ML) have impacted research communities based on statistical perspectives and uncovered invisibles from conventional standpoints. Though the field is still in the early stage, this progress has driven the thermal science and engineering communities to apply such cutting-edge toolsets for analyzing complex data, unraveling abstruse patterns, and discovering non-intuitive principles. In this work, we present a holistic overview of the applications and future opportunities of ML methods on crucial topics in thermal energy research, from bottom-up materials discovery to top-down system design across atomistic levels to multi-scales. In particular, we focus on a spectrum of impressive ML endeavors investigating the state-of-the-art thermal transport modeling (density functional theory, molecular dynamics, and Boltzmann transport equation), different families of materials (semiconductors, polymers, alloys, and composites), assorted aspects of thermal properties (conductivity, emissivity, stability, and thermoelectricity), and engineering prediction and optimization (devices and systems). We discuss the promises and challenges of current ML approaches and provide perspectives for future directions and new algorithms that could make further impacts on thermal energy research.

Computational UV spectra for amorphous solids of small molecules

Ices in the interstellar medium largely exist as amorphous solids composed of small molecules including ammonia, water, and carbon dioxide. Describing gas-phase molecules can be readily accomplished with current high-level quantum chemical calculations with the description of crystalline solids becoming more readily accomplished. Differently, amorphous solids require more novel approaches. The present work describes a method for generating amorphous structures and constructing electronic spectra through a combination of quantum chemical calculations and statistical mechanics. The structures are generated through a random positioning program and DFT methods, such as ωB97-XD and CAM-B3LYP. A Boltzmann distribution weights the excitations to compile a final spectrum from a sampling of molecular clusters. Three ice analogs are presented herein consisting of ammonia, carbon dioxide, and water. Ammonia and carbon dioxide provide semi-quantitative agreement with experiment for CAM-B3LYP/6-311++G(2d,2p) from 30 clusters of 8 molecules. Meanwhile, the amorphous water description improves when the sample size is increased in cluster size and count to as many as 105 clusters of 32 water molecules. The described methodology can produce highly comparative descriptions of electronic spectra for ice analogs and can be used to predict electronic spectra for other ice analogs.

Gaussian Process Regression for Materials and Molecules

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Machine-learned potentials for next-generation matter simulations

The choice of simulation methods in computational materials science is driven by a fundamental trade-off: bridging large time- and length-scales with highly accurate simulations at an affordable computational cost. Venturing the investigation of complex phenomena on large scales requires fast yet accurate computational methods. We review the emerging field of machine-learned potentials, which promises to reach the accuracy of quantum mechanical computations at a substantially reduced computational cost. This Review will summarize the basic principles of the underlying machine learning methods, the data acquisition process and active learning procedures. We highlight multiple recent applications of machine-learned potentials in various fields, ranging from organic chemistry and biomolecules to inorganic crystal structure predictions and surface science. We furthermore discuss the developments required to promote a broader use of ML potentials, and the possibility of using them to help solve open questions in materials science and facilitate fully computational materials design.

Inverse Design of Fe-Based Bulk Metallic Glasses Using Machine Learning

Fe-based bulk metallic glasses (BMGs) are a unique class of materials that are attracting attention in a wide variety of applications owing to their physical properties. Several studies have investigated and designed the relationships between alloy composition and thermal properties of BMGs using an artificial neural network (ANN). The limitation of the wide-scale use of these models is that the required composition is yet to be found despite numerous case studies. To address this issue, we trained an ANN to design Fe-based BMGs that predict the thermal properties. Models were trained using only the composition of the alloy as input and were created from a database of more than 150 experimental data of Fe-based BMGs from relevant literature. We adopted these ANN models to design BMGs with thermal properties to satisfy the intended purpose using particle swarm optimization. A melt spinner was employed to fabricate the designed alloys. X-ray diffraction and differential thermal analysis tests were used to evaluate the specimens.

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.

Measuring transferability issues in machine-learning force fields: the example of gold–iron interactions with linearized potentials

Machine-learning force fields have been increasingly employed in order to extend the possibility of current first-principles calculations. However, the transferability of the obtained potential cannot always be guaranteed in situations that are outside the original database. To study such limitation, we examined the very difficult case of the interactions in gold–iron nanoparticles. For the machine-learning potential, we employed a linearized formulation that is parameterized using a penalizing regression scheme which allows us to control the complexity of the obtained potential. We showed that while having a more complex potential allows for a better agreement with the training database, it can also lead to overfitting issues and a lower accuracy in untrained systems.

Prediction of optoelectronic properties of Cu2O using neural network potential

Neural network potentials (NNPs) trained against density functional theory (DFT) are capable of reproducing the potential energy surface at a fraction of the computational cost. However, most NNP implementations focus on energy and forces. In this work, we modified the NNP model introduced by Behler and Parrinello to predict Fermi energy, band edges, and partial density of states of Cu2O. Our NNP can reproduce the DFT potential energy surface and properties at a fraction of the computational cost. We used our NNP to perform molecular dynamics (MD) simulations and validated the predicted properties against DFT calculations. Our model achieved a root mean squared error of 16 meV for the energy prediction. Furthermore, we show that the standard deviation of the energies predicted by the ensemble of training snapshots can be used to estimate the uncertainty in the predictions. This allows us to switch from the NNP to DFT on-the-fly during the MD simulation to evaluate the forces when the uncertainty is high.

Machine-Learning Assisted Screening of Energetic Materials

In this work, machine learning (ML), materials informatics (MI), and thermochemical data are combined to screen potential candidates of energetic materials. To directly characterize energetic performance, the heat of explosion ΔH_e is used as the target property. The critical descriptors of cohesive energy, averaged over all constituent elements and the oxygen balance, are found by forward stepwise selection from a large number of possible descriptors. With them and a theoretically labeled ΔH_e training data set, a satisfactory surrogate ML model is trained. The ML model is applied to large databases ICSD and PubChem to predict ΔH_e. At the gross-level filtering by the ML model, 2732 molecular candidates based on carbon, hydrogen, nitrogen, and oxygen (CHNO) with high ΔH_e values are predicted. Afterward, a fine-level thermochemical screening is carried out on the 2732 materials, resulting in 262 candidates with TNT equivalent power index P_e(TNT) greater than 1.5. Raising P_e(TNT) further to larger than 1.8, 29 potential candidates are found from the 2732 materials, all are new to the current reservoir of well-known energetic materials.

Incorporating Electronic Information into Machine Learning Potential Energy Surfaces via Approaching the Ground-State Electronic Energy as a Function of Atom-Based Electronic Populations

Machine learning (ML) approximations to density functional theory (DFT) potential energy surfaces (PESs) are showing great promise for reducing the computational cost of accurate molecular simulations, but at present, they are not applicable to varying electronic states, and in particular, they are not well suited for molecular systems in which the local electronic structure is sensitive to the medium to long-range electronic environment. With this issue as the focal point, we present a new machine learning approach called "BpopNN" for obtaining efficient approximations to DFT PESs. Conceptually, the methodology is based on approaching the true DFT energy as a function of electron populations on atoms; in practice, this is realized with available density functionals and constrained DFT (CDFT). The new approach creates approximations to this function with neural networks. These approximations thereby incorporate electronic information naturally into a ML approach, and optimizing the model energy with respect to populations allows the electronic terms to self-consistently adapt to the environment, as in DFT. We confirm the effectiveness of this approach with a variety of calculations on Li_nH_n clusters.

Physical and chemical descriptors for predicting interfacial thermal resistance

Heat transfer at interfaces plays a critical role in material design and device performance. Higher interfacial thermal resistances (ITRs) affect the device efficiency and increase the energy consumption. Conversely, higher ITRs can enhance the figure of merit of thermoelectric materials by achieving ultra-low thermal conductivity via nanostructuring. This study proposes a dataset of descriptors for predicting the ITRs. The dataset includes two parts: one part consists of ITRs data collected from 87 experimental papers and the other part consists of the descriptors of 289 materials, which can construct over 80,000 pair-material systems for ITRs prediction. The former part is composed of over 1300 data points of metal/nonmetal, nonmetal/nonmetal, and metal/metal interfaces. The latter part consists of physical and chemical properties that are highly correlated to the ITRs. The synthesis method of the materials and the thermal measurement technique are also recorded in the dataset for further analyses. These datasets can be applied not only to ITRs predictions but also to thermal-property predictions or heat transfer on various material systems.

Measurement(s)	material entity • interface • Material Description
Technology Type(s)	machine learning • digital curation

Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.11618253

Machine Learning Interatomic Potentials as Emerging Tools for Materials Science

Atomic-scale modeling and understanding of materials have made remarkable progress, but they are still fundamentally limited by the large computational cost of explicit electronic-structure methods such as density-functional theory. This Progress Report shows how machine learning (ML) is currently enabling a new degree of realism in materials modeling: by "learning" electronic-structure data, ML-based interatomic potentials give access to atomistic simulations that reach similar accuracy levels but are orders of magnitude faster. A brief introduction to the new tools is given, and then, applications to some select problems in materials science are highlighted: phase-change materials for memory devices; nanoparticle catalysts; and carbon-based electrodes for chemical sensing, supercapacitors, and batteries. It is hoped that the present work will inspire the development and wider use of ML-based interatomic potentials in diverse areas of materials research.