Gaussian Approximation Potential Model Research Articles

Atomistic fracture in bcc iron revealed by active learning of Gaussian approximation potential

The prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip under mode-I loading based on empirical interatomic potentials yield contradicting predictions and artificial mechanisms. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a converged model uncertainty over a broad range of stress intensity factors (SIFs) and for four crack systems. The learning efficiency of the approach is analysed, and the predicted critical SIFs are compared with Griffith and Rice theories. The simulations reveal that cleavage along the original crack plane is the atomistic fracture mechanism for {100} and {110} crack planes at T = 0 K, thus settling a long-standing issue. Our work also highlights the need for a multiscale approach to predicting fracture and intrinsic ductility, whereby finite temperature, finite loading rate effects and pre-existing defects (e.g., nanovoids, dislocations) should be taken explicitly into account.

A machine-learned interatomic potential for silica and its relation to empirical models

Silica (SiO2) is an abundant material with a wide range of applications. Despite much progress, the atomistic modelling of the different forms of silica has remained a challenge. Here we show that by combining density-functional theory at the SCAN functional level with machine-learning-based interatomic potential fitting, a range of condensed phases of silica can be accurately described. We present a Gaussian approximation potential model that achieves high accuracy for the thermodynamic properties of the crystalline phases, and we compare its performance (and performance–cost trade-off) with that of multiple empirically fitted interatomic potentials for silica. We also include amorphous phases, assessing the ability of the potentials to describe structures of melt-quenched glassy silica, their energetic stability, and the high-pressure structural transition to a mainly sixfold-coordinated phase. We suggest that rather than standing on their own, machine-learned potentials for silica may be used in conjunction with suitable empirical models, each having a distinct role and complementing the other, by combining the advantages of the long simulation times afforded by empirical potentials and the near-quantum-mechanical accuracy of machine-learned potentials. This way, our work is expected to advance atomistic simulations of this key material and to benefit further computational studies in the field.

Developing machine learning potential for classical molecular dynamics simulation with superior phonon properties

Classical molecular dynamics is one of the most important methods for exploring material properties and uncovering physical mechanism, but the predicted results strongly depend on the used potentials. Using ab initio molecular dynamics simulations to obtain atomic conformations and the associated energy and force as training set and testing set, we developed a Gaussian approximation potential model for single-layer MoS2based on the machine learning method. The phonon dispersion relations calculated from the developed potential are compared well to that of density functional theory,which confirms the accuracy of the developed potential in the harmonic interaction. We also calculated the temperature-dependent Raman-active phonon frequency and linewidth of the single-layer MoS2 using classical molecular dynamics. The obtained temperature-dependent phonon frequency and linewidth are compared with the corresponding experimental results, indicating that the developed potential still has high accuracy in the anharmonic interactions. The detailed process and methods to obtain the MoS2potential in this work can be extended and applied to the development and investigation of the high-precision potential of emerging new materials.

Machine learning driven simulated deposition of carbon films: From low-density to diamondlike amorphous carbon

Amorphous carbon (a-C) materials have diverse interesting and useful properties, but the understanding of their atomic-scale structures is still incomplete. Here, we report on extensive atomistic simulations of the deposition and growth of a-C films, describing interatomic interactions using a machine learning (ML) based Gaussian approximation potential model. We expand widely on our initial work [M. A. Caro et al., Phys. Rev. Lett. 120, 166101 (2018)] by now considering a broad range of incident ion energies, thus modeling samples that span the entire range from low-density ($s{p}^{2}$-rich) to high-density ($s{p}^{3}$-rich, ``diamondlike'') amorphous forms of carbon. Two different mechanisms are observed in these simulations, depending on the impact energy: low-energy impacts induce $sp$- and $s{p}^{2}$-dominated growth directly around the impact site, whereas high-energy impacts induce peening. Furthermore, we propose and apply a scheme for computing the anisotropic elastic properties of the a-C films. Our work provides fundamental insight into this intriguing class of disordered solids, as well as a conceptual and methodological blueprint for simulating the atomic-scale deposition of other materials with ML driven molecular dynamics.

Machine learning interatomic potential developed for molecular simulations on thermal properties of β-Ga2O3.

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.

Combining phonon accuracy with high transferability in Gaussian approximation potential models.

Machine learning driven interatomic potentials, including Gaussian approximation potential (GAP) models, are emerging tools for atomistic simulations. Here, we address the methodological question of how one can fit GAP models that accurately predict vibrational properties in specific regions of configuration space while retaining flexibility and transferability to others. We use an adaptive regularization of the GAP fit that scales with the absolute force magnitude on any given atom, thereby exploring the Bayesian interpretation of GAP regularization as an "expected error" and its impact on the prediction of physical properties for a material of interest. The approach enables excellent predictions of phonon modes (to within 0.1 THz-0.2 THz) for structurally diverse silicon allotropes, and it can be coupled with existing fitting databases for high transferability across different regions of configuration space, which we demonstrate for liquid and amorphous silicon. These findings and workflows are expected to be useful for GAP-driven materials modeling more generally.

Machine-learned interatomic potentials by active learning: amorphous and liquid hafnium dioxide

We propose an active learning scheme for automatically sampling a minimum number of uncorrelated configurations for fitting the Gaussian Approximation Potential (GAP). Our active learning scheme consists of an unsupervised machine learning (ML) scheme coupled with a Bayesian optimization technique that evaluates the GAP model. We apply this scheme to a Hafnium dioxide (HfO2) dataset generated from a “melt-quench” ab initio molecular dynamics (AIMD) protocol. Our results show that the active learning scheme, with no prior knowledge of the dataset, is able to extract a configuration that reaches the required energy fit tolerance. Further, molecular dynamics (MD) simulations performed using this active learned GAP model on 6144 atom systems of amorphous and liquid state elucidate the structural properties of HfO2 with near ab initio precision and quench rates (i.e., 1.0 K/ps) not accessible via AIMD. The melt and amorphous X-ray structural factors generated from our simulation are in good agreement with experiment. In addition, the calculated diffusion constants are in good agreement with previous ab initio studies.

Optimizing many-body atomic descriptors for enhanced computational performance of machine learning based interatomic potentials

We explore different ways to simplify the evaluation of the smooth overlap of atomic positions (SOAP) many-body atomic descriptor [Bart\'{o}k et al., Phys. Rev. B 87, 184115 (2013)]. Our aim is to improve the computational efficiency of SOAP-based similarity kernel construction. While these improved atomic descriptors can be used for general characterization and interpolation of atomic properties, their main target application is accelerated evaluation of machine-learning-based interatomic potentials within the Gaussian approximation potential (GAP) framework [Bart\'{o}k et al., Phys. Rev. Lett. 104, 136403 (2010)]. We achieve this objective by expressing the atomic densities in an approximate separable form, which decouples the radial and angular channels. We then express the elements of the SOAP descriptor (i.e., the expansion coefficients for the atomic densities) in analytical form given a particular choice of radial basis set. Finally, we derive recursion formulas for the expansion coefficients. This new SOAP-based descriptor allows for tenfold speedups compared to previous implementations, while improving the stability of the radial expansion for distant atomic neighbors, without degradation of the interpolation power of GAP models.

Gaussian approximation potential modeling of lithium intercalation in carbon nanostructures.

We demonstrate how machine-learning based interatomic potentials can be used to model guest atoms in host structures. Specifically, we generate Gaussian approximation potential (GAP) models for the interaction of lithium atoms with graphene, graphite, and disordered carbon nanostructures, based on reference density functional theory data. Rather than treating the full Li-C system, we demonstrate how the energy and force differences arising from Li intercalation can be modeled and then added to a (prexisting and unmodified) GAP model of pure elemental carbon. Furthermore, we show the benefit of using an explicit pair potential fit to capture "effective" Li-Li interactions and to improve the performance of the GAP model. This provides proof-of-concept for modeling guest atoms in host frameworks with machine-learning based potentials and in the longer run is promising for carrying out detailed atomistic studies of battery materials.

Development of a machine learning potential for graphene

We present an accurate interatomic potential for graphene, constructed using the Gaussian Approximation Potential (GAP) machine learning methodology. This GAP model obtains a faithful representation of a density functional theory (DFT) potential energy surface, facilitating highly accurate (approaching the accuracy of ab initio methods) molecular dynamics simulations. This is achieved at a computational cost which is orders of magnitude lower than that of comparable calculations which directly invoke electronic structure methods. We evaluate the accuracy of our machine learning model alongside that of a number of popular empirical and bond-order potentials, using both experimental and ab initio data as references. We find that whilst significant discrepancies exist between the empirical interatomic potentials and the reference data - and amongst the empirical potentials themselves - the machine learning model introduced here provides exemplary performance in all of the tested areas. The calculated properties include: graphene phonon dispersion curves at 0 K (which we predict with sub-meV accuracy), phonon spectra at finite temperature, in-plane thermal expansion up to 2500 K as compared to NPT ab initio molecular dynamics simulations and a comparison of the thermally induced dispersion of graphene Raman bands to experimental observations. We have made our potential freely available online at [http://www.libatoms.org].

Machine learning based interatomic potential for amorphous carbon

We introduce a Gaussian approximation potential (GAP) for atomistic simulations of liquid and amorphous elemental carbon. Based on a machine-learning representation of the density-functional theory (DFT) potential-energy surface, such interatomic potentials enable materials simulations with close-to DFT accuracy but at much lower computational cost. We first determine the maximum accuracy that any finite-range potential can achieve in carbon structures; then, using a novel hierarchical set of two-, three-, and many-body structural descriptors, we construct a GAP model that can indeed reach the target accuracy. The potential yields accurate energetic and structural properties over a wide range of densities; it also correctly captures the structure of the liquid phases, at variance with state-of-the-art empirical potentials. Exemplary applications of the GAP model to surfaces of "diamond-like" tetrahedral amorphous carbon (ta-C) are presented, including an estimate of the amorphous material's surface energy, and simulations of high-temperature surface reconstructions ("graphitization"). The new interatomic potential appears to be promising for realistic and accurate simulations of nanoscale amorphous carbon structures.

Accuracy and transferability of Gaussian approximation potential models for tungsten

We introduce interatomic potentials for tungsten in the bcc crystal phase and its defects within the Gaussian approximation potential framework, fitted to a database of first-principles density functional theory calculations. We investigate the performance of a sequence of models based on databases of increasing coverage in configuration space and showcase our strategy of choosing representative small unit cells to train models that predict properties observable only using thousands of atoms. The most comprehensive model is then used to calculate properties of the screw dislocation, including its structure, the Peierls barrier and the energetics of the vacancy-dislocation interaction. All software and raw data are available at www.libatoms.org.