Abstract: Molecular dynamics simulations have emerged as a potent tool for investigating the physical properties and kinetic behaviors of materials at the atomic scale, particularly in extreme conditions. Ab initio accuracy is now achievable with machine learning based interatomic potentials. With recent advancements in high-performance computing, highly accurate and large-scale simulations become feasible. This study introduces TensorMD, a new machine learning interatomic potential (MLIP) model that integrates physical principles and tensor diagrams. The tensor formalism provides a more efficient computation and greater flexibility for use with other scientific codes. Additionally, we proposed several portable optimization strategies and developed a highly optimized version for the new Sunway supercomputer. Our optimized TensorMD can achieve unprecedented performance on the new Sunway, enabling simulations of up to 52 billion atoms with a time-to-solution of 31 ps/step/atom, setting new records for HPC + AI + MD. read less

Abstract: ABSTRACT Recently, machine learning potentials (MLPs) have been attracting interest as an alternative to the computationally expensive density-functional theory (DFT) calculations. The data-driven approach in MLPs requires carefully curated training datasets, which define the valid domain of simulations. Therefore, acquiring training datasets that comprehensively span the domain of the desired simulations is important. In this review, we attempt to set guidelines for the systematic construction of training datasets according to target simulations. To this end, we extensively analyze the training sets in previous literature according to four application types: thermal properties, diffusion properties, structure prediction, and chemical reactions. In each application, we summarize characteristic reference structures and discuss specific parameters for DFT calculations such as MD conditions. We hope this review serves as a comprehensive guide for researchers and practitioners aiming to harness the capabilities of MLPs in material simulations. IMPACT STATEMENT This review reports on the selection of training sets for machine learning potentials tailored to their specific applications, which is currently not standardized in the rapidly evolving field. read less

Abstract: Mg3(Sb1-xBix)2 alloy has been extensively studied in the last 5 years due to its exceptional thermoelectric (TE) performance. The absence of accurate force field for inorganic alloy compounds presents great challenges for computational studies. Here, we explore the atomic microstructure, thermal, and elastic properties of the Mg3(Sb1-xBix)2 alloy at different solution concentrations through atomic simulations with a highly accurate machine learning interatomic potential (ML-IAP). We find atomic local ordering in the optimized structure with the Bi-Bi pair inclined to join adjacent layers and Sb-Sb pair preferring to stay within the same layer. The thermal conductivity changes with the solution concentrations can be correctly predicted through ML-IAP-based molecular dynamics simulations. Spectral thermal conductance analysis shows that the continuous movement of low-frequency peak to high frequency is responsible for the reduction of the thermal conductivity upon alloying. Elastic calculations reveal that similar to the thermal conductivity, solid solution alloying can reduce the overall elastic properties at both Mg3Sb2 and Mg3Bi2 ends, while anisotropic behavior is clearly observed with linear interpolation relationship upon alloying along the interlayer direction and nonlinearity along the intralayer direction. Although the atomic local ordering shows little effects on the properties of the Mg3(Sb1-xBix)2 alloy with only two alloying elements, it possesses potential important impacts on multiprincipal element inorganic TE alloys. This work provides a recipe for computational studies on the TE alloy systems and thus can accelerate the discovery and optimization of TE materials with high TE performance. read less

Abstract: Sulfide-based glasses and glass-ceramics showing high ionic conductivities and excellent mechanical properties are considered as promising solid-state electrolytes. Nowadays, the computational material techniques with the advantage of low research cost... read less

Abstract: To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials. read less

Abstract: Zr–Rh metallic glass has enabled its many applications in vehicle parts, sports equipment and so on due to its outstanding performance in mechanical property, but the knowledge of the microstructure determining the superb mechanical property remains yet insufficient. Here, we develop a deep neural network potential of Zr–Rh system by using machine learning, which breaks the dilemma between the accuracy and efficiency in molecular dynamics simulations, and greatly improves the simulation scale in both space and time. The results show that the structural features obtained from the neural network method are in good agreement with the cases in ab initio molecular dynamics simulations. Furthermore, we build a large model of 5400 atoms to explore the influences of simulated size and cooling rate on the melt-quenching process of Zr77Rh23. Our study lays a foundation for exploring the complex structures in amorphous Zr77Rh23, which is of great significance for the design and practical application. read less

Abstract: The use of machine learning to develop neural network potentials (NNP) representing the interatomic potential energy surface allows us to achieve an optimal balance between accuracy and efficiency in computer simulation of materials. A key point in developing such potentials is the preparation of a training dataset of ab initio trajectories. Here we apply a deep potential molecular dynamics (DeePMD) approach to develop NNP for silica, which is the representative glassformer widely used as a model system for simulating network-forming liquids and glasses. We show that the use of a relatively small training dataset of high-temperature ab initio configurations is enough to fabricate NNP, which describes well both structural and dynamical properties of liquid silica. In particular, we calculate the pair correlation functions, angular distribution function, velocity autocorrelation functions, vibrational density of states, and mean-square displacement and reveal a close agreement with ab initio data. We show that NNP allows us to expand significantly the time-space scales achievable in simulations and thus calculating dynamical and transport properties with more accuracy than that for ab initio methods. We find that developed NNP allows us to describe the structure of the glassy silica with satisfactory accuracy even though no low-temperature configurations were included in the training procedure. The results obtained open up prospects for simulating structural and dynamical properties of liquids and glasses via NNP. read less

Abstract: We present PyXtal_FF—a package based on Python programming language—for developing machine learning potentials (MLPs). The aim of PyXtal_FF is to promote the application of atomistic simulations through providing several choices of atom-centered descriptors and machine learning regressions in one platform. Based on the given choice of descriptors (including the atom-centered symmetry functions, embedded atom density, SO4 bispectrum, and smooth SO3 power spectrum), PyXtal_FF can train MLPs with either generalized linear regression or neural network models, by simultaneously minimizing the errors of energy/forces/stress tensors in comparison with the data from ab-initio simulations. The trained MLP model from PyXtal_FF is interfaced with the Atomic Simulation Environment (ASE) package, which allows different types of light-weight simulations such as geometry optimization, molecular dynamics simulation, and physical properties prediction. Finally, we will illustrate the performance of PyXtal_FF by applying it to investigate several material systems, including the bulk SiO2, high entropy alloy NbMoTaW, and elemental Pt for general purposes. Full documentation of PyXtal_FF is available at https://pyxtal-ff.readthedocs.io. read less

Abstract: Since its development in the 1970s, the rechargeable alkali-ion battery has proven to be a truly transformative technology, providing portable energy storage for devices ranging from small portable electronics to sizable electric vehicles. Here, we present a review of modern theoretical and computational approaches to the study and design of rechargeable alkali-ion battery materials. Starting from fundamental thermodynamics and kinetics phenomenological equations, we rigorously derive the theoretical relationships for key battery properties, such as voltage, capacity, alkali diffusivity, and other electrochemically relevant computable quantities. We then present an overview of computational techniques for the study of rechargeable alkali-ion battery materials, followed by a critical review of the literature applying these techniques to yield crucial insights into battery operation and performance. Finally, we provide perspectives on outstanding challenges and opportunities in the theory and computation of rechargeable alkali-ion battery materials. read less

Abstract: Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of ML-IAPs based on four local environment descriptors --- atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the Spectral Neighbor Analysis Potential (SNAP) bispectrum components, and moment tensors --- using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model, and consequently computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications. read less

Abstract: The prediction of phase diagrams in the search for new phases is a complex and computationally intensive task. Density functional theory provides, in many situations, the desired accuracy, but its throughput becomes prohibitively limited as the number of species involved grows, even when used with local and semi-local functionals. Here, we explore the possibility of integrating machine-learning models in the workflow for the construction of ternary convex hull diagrams. In particular, we train a set of spectral neighbour-analysis potentials (SNAPs) over readily available binary phases and we establish whether this is good enough to predict the energies of novel ternaries. Such a strategy does not require any new calculations specific for the construction of the model, but just avails of data stored in binary-phase-diagram repositories. We find that a so-constructed SNAP is capable of accurate total-energy estimates for ternary phases close to the equilibrium geometry but, in general, is not able to perform atomic relaxation. This is because during a typical relaxation path a given phase traverses regions in the parameter space poorly represented by the training set. Different metrics are then investigated to assess how an unknown structure is well described by a given SNAP model, and we find that the standard deviation of an ensemble of SNAPs provides a fast and non-specie-specific metric. read less

Abstract: Predicting UV-visible absorption spectra is essential to understand photochemical processes and design energy materials. Quantum chemical methods can deliver accurate calculations of UV-visible absorption spectra, but they are computationally expensive, especially for large systems or when one computes line shapes from thermal averages. Here, we present an approach to predict UV-visible absorption spectra of solvated aromatic molecules by quantum chemistry (QC) and machine learning (ML). We show that a ML model, trained on the high-level QC calculation of the excitation energy of a set of aromatic molecules, can accurately predict the line shape of the lowest-energy UV-visible absorption band of several related molecules with less than 0.1 eV deviation with respect to reference experimental spectra. Applying linear decomposition analysis on the excitation energies, we unveil that our ML models probe vertical excitations of these aromatic molecules primarily by learning the atomic environment of their phenyl rings, which align with the physical origin of the π →π* electronic transition. Our study provides an effective workflow that combines ML with quantum chemical methods to accelerate the calculations of UV-visible absorption spectra for various molecular systems. read less

Abstract: This paper summarizes the progress of machine‐learning‐based interatomic potentials and their applications in advanced manufacturing. Interatomic potential is essential for classical molecular dynamics. The advancements made in machine learning (ML) have enabled the development of fast interatomic potential with ab initio accuracy. The accelerated atomic simulation can greatly transform the design principle of manufacturing technology. The most widely used supervised and unsupervised ML methods are summarized and compared. Then, the emerging interatomic models based on ML are discussed: Gaussian approximation potential, spectral neighbor analysis potential, deep potential molecular dynamics, SCHNET, hierarchically interacting particle neural network, and fast learning of atomistic rare events. read less

Abstract: The thermal properties of β-Ga2O3 can significantly affect the performance and reliability of high-power electronic devices. To date, due to the absence of a reliable interatomic potential, first-principles calculations based on density functional theory (DFT) have been routinely used to probe the thermal properties of β-Ga2O3. DFT calculations can only tackle small-scale systems due to the huge computational cost, while the thermal transport processes are usually associated with large time and length scales. In this work, we develop a machine learning based Gaussian approximation potential (GAP) for accurately describing the lattice dynamics of perfect crystalline β-Ga2O3 and accelerating atomic-scale simulations. The GAP model shows excellent convergence, which can faithfully reproduce the DFT potential energy surface at a training data size of 32 000 local atomic environments. The GAP model is then used to predict ground-state lattice parameters, coefficients of thermal expansion, heat capacity, phonon dispersions at 0 K, and anisotropic thermal conductivity of β-Ga2O3, which are all in excellent agreement with either the DFT results or experiments. The accurate predictions of phonon dispersions and thermal conductivities demonstrate that the GAP model can well describe the harmonic and anharmonic interactions of phonons. Additionally, the successful application of our GAP model to the phonon density of states of a 2500-atom β-Ga2O3 structure at elevated temperature indicates the strength of machine learning potentials to tackle large-scale atomic systems in long molecular simulations, which would be almost impossible to generate with DFT-based molecular simulations at present. read less

Abstract: Interatomic potentials constitute the key component of large-scale atomistic simulations of materials. The recently proposed physically-informed neural network (PINN) method combines a high-dimensional regression implemented by an artificial neural network with a physics-based bond-order interatomic potential applicable to both metals and nonmetals. In this paper, we present a modified version of the PINN method that accelerates the potential training process and further improves the transferability of PINN potentials to unknown atomic environments. As an application, a modified PINN potential for Al has been developed by training on a large database of electronic structure calculations. The potential reproduces the reference first-principles energies within 2.6 meV per atom and accurately predicts a wide spectrum of physical properties of Al. Such properties include, but are not limited to, lattice dynamics, thermal expansion, energies of point and extended defects, the melting temperature, the structure and dynamic properties of liquid Al, the surface tensions of the liquid surface and the solid-liquid interface, and the nucleation and growth of a grain boundary crack. Computational efficiency of PINN potentials is also discussed. read less

Abstract: The miscibility of Au and Li exhibits a potential application as an adhesion layer and electrode material in secondary batteries. Here, to explore alloying properties, we constructed a neural network potential (NNP) of Au-Li binary systems based on density functional theory (DFT) calculations. To accelerate construction of NNPs, we proposed an efficient and inexpensive method of structural dataset generation. The predictions by the constructed NNP on lattice parameters and phonon properties agree well with those obtained by DFT calculations. We also investigated the mixing energy of Au$_{1-x}$Li$_{x}$ with fine composition grids, showing excellent agreement with DFT verifications. We found the existence of various compositions with structures on and slightly above the convex hull, which can explain the lack of consensus on the Au-Li stable phases in previous studies. Moreover, we newly found Au$_{0.469}$Li$_{0.531}$ as a stable phase, which has never been reported elsewhere. Finally, we examined the alloying process starting from the phase separated structure to the complete mixing phase. We found that when multiple adjacent Au atoms dissolved into Li, the alloying of the entire Au/Li interface started from the dissolved region. This paper demonstrates the applicability of NNPs toward miscible phases and provides the understanding of the alloying mechanism. read less

Abstract: In this work, we present a numerical implementation to compute the atom centered descriptors introduced by Bartok et al (Phys. Rev. B, 87, 184115, 2013) based on the harmonic analysis of the atomic neighbor density function. Specifically, we focus on two types of descriptors, the smooth SO(3) power spectrum with the explicit inclusion of a radial basis and the SO(4) bispectrum obtained through mapping the radial component onto a polar angle of a four dimensional hypersphere. With these descriptors, various interatomic potentials for binary Ni-Mo alloys are obtained based on linear and neural network regression models. Numerical experiments suggest that both descriptors produce similar results in terms of accuracy. For linear regression, the smooth SO(3) power spectrum is superior to the SO(4) bispectrum when a large band limit is used. In neural network regression, a better accuracy can be achieved with even less number of expansion components for both descriptors. As such, we demonstrate that spectral neural network potentials are feasible choices for large scale atomistic simulation. read less

Abstract: A natural extension of the descriptors used in the Spectral Neighbor Analysis Potential (SNAP) method is derived to treat atomic interactions in chemically complex systems. Atomic environment descriptors within SNAP are obtained from a basis function expansion of the weighted density of neighboring atoms. This new formulation instead partitions the neighbor density into partial densities for each chemical element, thus leading to explicit multi-element descriptors. For Nelem chemical elements, the number of descriptors increases as Ο(Nelem3), while the computational cost of the force calculation as implemented in LAMMPS is limited to Ο(Nelem2) and the favorable linear scaling in the number of atoms is retained. We demonstrate these chemically aware descriptors by producing an interatomic potential for indium phosphide capable of capturing high-energy defects that result from radiation damage cascades. This new explicit multi-element SNAP method reproduces the relaxed defect formation energies with substantially greater accuracy than weighted-density SNAP, while retaining accurate representation of the bulk indium phosphide properties. read less

Abstract: The use of supervised machine learning to develop fast and accurate interatomic potential models is transforming molecular and materials research by greatly accelerating atomic-scale simulations with little loss of accuracy. Three years ago, Jörg Behler published a perspective in this journal providing an overview of some of the leading methods in this field. In this perspective, we provide an updated discussion of recent developments, emerging trends, and promising areas for future research in this field. We include in this discussion an overview of three emerging approaches to developing machine-learned interatomic potential models that have not been extensively discussed in existing reviews: moment tensor potentials, message-passing networks, and symbolic regression. read less

Abstract: Machine learning (ML) is rapidly revolutionizing many fields and is starting to change landscapes for physics and chemistry. With its ability to solve complex tasks autonomously, ML is being exploited as a radically new way to help find material correlations, understand materials chemistry, and accelerate the discovery of materials. Here, an in‐depth review of the application of ML to energy materials, including rechargeable alkali‐ion batteries, photovoltaics, catalysts, thermoelectrics, piezoelectrics, and superconductors, is presented. A conceptual framework is first provided for ML in materials science, with a broad overview of different ML techniques as well as best practices. This is followed by a critical discussion of how ML is applied in energy materials. This review is concluded with the perspectives on major challenges and opportunities in this exciting field. read less

Abstract: Interatomic potentials based on neural-network machine learning (ML) approach to address the longstanding challenge of accuracy versus efficiency in molecular-dynamics simulations have recently attracted a great deal of interest. Here, utilizing Pd-Si system as a prototype, we extend the development of neural-network ML potentials to compounds exhibiting various types of bonding characteristics. The ML potential is trained by fitting to the energies and forces of both liquid and crystal structures firstprinciples calculations based on density-functional theory (DFT). We show that the generated ML potential captures the structural features and motifs in Pd82Si18 and Pd75Si25 liquids more accurately than the existing interatomic potential based on embedded-atom method (EAM). The ML potential also describes the solid-liquid interface of these systems very well. Moreover, while the existing EAM potential fails to describe the relative energies of various crystalline structures and predict wrong ground-state structures at Pd3Si and Pd9Si2 composition, the developed ML potential predicts correctly the groundstate structures from genetic algorithm search. The efficient ML potential with DFT accuracy from our study will provide a promising scheme for accurate atomistic simulations of structures and dynamics of complex Pd-Si system. Disciplines Condensed Matter Physics Authors Tongqi Wen, Cai-Zhuang Wang, Matthew J. Kramer, Yang Sun, Beilin Ye, Haidi Wang, Xueyuan Liu, Chao Zhang, Feng Zhang, Kai-Ming Ho, and Nan Wang This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/ameslab_manuscripts/ 663 PHYSICAL REVIEW B 100, 174101 (2019) Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds Tongqi Wen ,1,2 Cai-Zhuang Wang,2,3,* M. J. Kramer ,2 Yang Sun ,2 Beilin Ye,4 Haidi Wang,2 Xueyuan Liu,2 Chao Zhang ,2,5 Feng Zhang,2 Kai-Ming Ho,2,3 and Nan Wang 1,† 1MOE Key Laboratory of Materials Physics and Chemistry under Extraordinary Conditions, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an 710072, China 2Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA 3Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA 4School of Materials Science and Engineering, South China University of Technology, Guangzhou 510641, China 5Department of Physics, School of Opto-electronic Information Science and Technology, Yantai University, Yantai, 264005, China (Received 16 July 2019; revised manuscript received 8 October 2019; published 4 November 2019) Interatomic potentials based on neural-network machine learning (ML) approach to address the long-standing challenge of accuracy versus efficiency in molecular-dynamics simulations have recently attracted a great deal of interest. Here, utilizing Pd-Si system as a prototype, we extend the development of neural-network ML potentials to compounds exhibiting various types of bonding characteristics. The ML potential is trained by fitting to the energies and forces of both liquid and crystal structures first-principles calculations based on density-functional theory (DFT). We show that the generated ML potential captures the structural features and motifs in Pd82Si18 and Pd75Si25 liquids more accurately than the existing interatomic potential based on embedded-atom method (EAM). The ML potential also describes the solid-liquid interface of these systems very well. Moreover, while the existing EAM potential fails to describe the relative energies of various crystalline structures and predict wrong ground-state structures at Pd3Si and Pd9Si2 composition, the developed ML potential predicts correctly the ground-state structures from genetic algorithm search. The efficient ML potential with DFT accuracy from our study will provide a promising scheme for accurate atomistic simulations of structures and dynamics of complex Pd-Si system. DOI: 10.1103/PhysRevB.100.174101 read less

Abstract: Structural phase transitions as a function of temperature dictate the structure--functionality relationships in many technologically important materials. Harmonic Hamiltonians have proven successful in predicting the vibrational properties of many materials. However, they are inadequate for modeling structural phase transitions in crystals with potential energy surfaces that are either strongly anharmonic or no\ n-convex with respect to collective atomic displacements or homogeneous strains. In this paper we develop a framework to express highly anharmonic first-principles potential energy surfaces as polynomials of collective cluster deformati\ ons. We further adapt the approach to a nonlinear extension of the cluster expansion formalism through the use of an artificial neural net model. The machine learning models are trained on a large database of first-principles calculations and are shown to reproduce the potential energy surface with l\ ow error. read less

Abstract: Lattice structures, defect structures, and deformation mechanisms of high-entropy alloys (HEAs) have been studied using atomistic simulations to explain their remarkable mechanical properties. These atomistic simulation techniques, such as first-principles calculations and molecular dynamics allow atomistic-level resolution of structure, defect configuration, and energetics. Following the structure–property paradigm, such understandings can be useful for guiding the design of high-performance HEAs. Although there have been a number of atomistic studies on HEAs, there is no comprehensive review on the state-of-the-art techniques and results of atomistic simulations of HEAs. This article is intended to fill the gap, providing an overview of the state-of-the-art atomistic simulations on HEAs. In particular, we discuss how atomistic simulations can elucidate the nanoscale mechanisms of plasticity underlying the outstanding properties of HEAs, and further present a list of interesting problems for forthcoming atomistic simulations of HEAs. read less

Abstract: The central approximation made in classical molecular dynamics simulation of materials is the interatomic potential used to calculate the forces on the atoms. Great effort and ingenuity is required to construct viable functional forms and find accurate parametrizations for potentials using traditional approaches. Machine learning has emerged as an effective alternative approach to develop accurate and robust interatomic potentials. Starting with a very general model form, the potential is learned directly from a database of electronic structure calculations and therefore can be viewed as a multiscale link between quantum and classical atomistic simulations. Risk of inaccurate extrapolation exists outside the narrow range of time and length scales where the two methods can be directly compared. In this work, we use the spectral neighbor analysis potential (SNAP) and show how a fit can be produced with minimal interpolation errors which is also robust in extrapolating beyond training. To demonstrate the method, we have developed a tungsten-beryllium potential suitable for the full range of binary compositions. Subsequently, large-scale molecular dynamics simulations were performed of high energy Be atom implantation onto the (001) surface of solid tungsten. The machine learned W-Be potential generates a population of implantation structures consistent with quantum calculations of defect formation energies. A very shallow ($l2\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$) average Be implantation depth is predicted which may explain ITER diverter degradation in the presence of beryllium. read less