Gaussian Approximation Potential Research Articles

Constructing and Evaluating Machine-Learned Interatomic Potentials for Li-Based Disordered Rocksalts.

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

An investigation of self-interstitial diffusion in α-zirconium by an on-the-fly machine learning force field

The on-the-fly machine learning force field approach, based on the Gaussian approximation potential and Bayesian error estimation, was used to study the diffusion of self-interstitial atoms in α-zirconium. Ab initio molecular dynamics simulations of lattice vibration and interstitial diffusion at different temperatures were employed to develop the force field. The radial and angular descriptors of the potential were further optimized to achieve better agreement with first-principles results. Subsequent long-term diffusion simulations were performed to assess the diffusion behavior based on the obtained force field. Tracer diffusion coefficients and diffusion anisotropy were studied at temperatures of 600–1200 K, and the Bayesian errors were estimated throughout the diffusion simulations. The mean and maximum estimated Bayesian errors of atomic force were approximately twice as large as those observed during the learning period. The basal diffusion was greatly favored compared to the interstitial diffusion along the c-axis, consistent with previous simulations based on first-principles results and classical potentials. The accuracy and applicability of the current on-the-fly machine learning approach were critically evaluated.

Machine-Learned Potential Energy Surfaces for Free Sodium Clusters with Density Functional Accuracy: Applications to Melting

Gaussian Process Regression based Gaussian Approximation Potential has been used to develop machine learned interatomic potentials having density functional accuracy, for free sodium clusters. The training data was generated from a large sample of over 100,000 data points computed for clusters in the size range of N = 40–200, where N denotes the number of atoms in the cluster, using the density functional method as implemented in the VASP code. Two models have been developed, model M1 using data for N = 55 only, and model M2 using additional data from larger clusters. The models are intended for computing thermodynamic properties using molecular dynamics. Hence, particular attention has been paid to improve the fitting of the forces. Although it was possible to obtain a good fit using the data of Na55 only, additional data points from larger clusters were needed to get better accuracies in energies and forces for larger sizes. Surprisingly, the model M1 could be significantly improved by adding about 50 data points per cluster from the larger sizes. Thus, it turns out that the best fit can be obtained by carefully selecting a small number of data points viz. 1,900 and 1,300 configurations for the two models M1 and M2, respectively. These two models have been deployed to compute the heat capacities of Na55. The heat capacities of Na147 and about 40 isomers for larger clusters of sizes N = 147, 200, 201, and 252, have been obtained using the final model M2. There is an excellent agreement between the computed and experimentally measured melting temperatures. The geometries of these isomers have been further optimized by density functional theory. The mean absolute error with respect to DFT energies is found to be about 7 meV/atom or less. The errors in the lowest interatomic bond lengths are below 2% in almost all the cases.

A close-packed sphere model for characterising porous networks in atomistic simulations and its application in energy storage and conversion

Hierarchical (micro, meso & macro) porosity in materials plays a crucial role in influencing the movement of ions which governs the energy and power density during energy storage and conversion. The extant available methods to characterise porosity across scales (nano to meso to macro) lacks rigour and accuracy. Having accurate assessment of the porosity in materials can unlock new designs of electrodes for energy efficient energy storage and conversion devices such as batteries, supercapacitors and fuel cells. Through this work, we report the systematic development of a method to fully characterise the carbon porous networks using a molecular dynamics simulation testbed. Our work entails modelling and simulation of porous carbon structures using quenched molecular dynamics (QMD) simulations using Gaussian Approximation potential (GAP) and benchmarking the results with prior literature. This modelling technique can reliably be used for quantitative characterisation of the interconnectivity in porous structures to study ionic movements and charge transfer mechanisms. A new parameter, namely nearest neighbour search (NNS) coefficient was introduced to quantify homogeneity and networking in the porous structures. NNS coefficient increased from 1.62 to 1.92 with decrease of the annealing temperature from 8000 K to 4000 K in carbon. The procedure outlined was although tested on porous carbon networks, but adaptable to study any other material system at multi-length scales.

Impact of hydrogenation on the stability and mechanical properties of amorphous boron nitride

Interconnect materials with ultralow dielectric constant, and good thermal and mechanical properties are crucial for the further miniaturization of electronic devices. Recently, it has been demonstrated that ultrathin amorphous boron nitride (aBN) films have a very low dielectric constant, high density (above 2.1 g cm−3), high thermal stability, and mechanical properties. The excellent properties of aBN derive from the nature and degree of disorder, which can be controlled at fabrication, allowing tuning of the physical properties for desired applications. Here, we report an improvement in the stability and mechanical properties of aBN upon hydrogen doping. With the introduction of a Gaussian approximation potential for atomistic simulations, we investigate the changing morphology of aBN with varying H doping concentrations. We found that for 8 at% of H doping, the concentration of sp 3-hybridized atoms reaches to a maximum which leads to an improvement of thermal stability and mechanical properties by 20%. These results will be a guideline for experimentalists and process engineers to tune the growth conditions of aBN films for numerous applications.

Active machine learning model for the dynamic simulation and growth mechanisms of carbon on metal surface

Substrate-catalyzed growth offers a highly promising approach for the controlled synthesis of carbon nanostructures. However, the growth mechanisms on dynamic catalytic surfaces and the development of more general design strategies remain ongoing challenges. Here we show how an active machine-learning model effectively reveals the microscopic processes involved in substrate-catalyzed growth. Utilizing a synergistic approach of molecular dynamics and time-stamped force-biased Monte Carlo methods, augmented by the Gaussian Approximation Potential, we perform fully dynamic simulations of graphene growth on Cu(111). Our findings accurately replicate essential subprocesses–from the preferred diffusion of carbon monomer/dimer, chain or ring formations to edge-passivated Cu-aided graphene growth and bond breaks by ion impacts. Extending our simulations to carbon deposition on metal surfaces like Cu(111), Cr(110), Ti(001), and oxygen-contaminated Cu(111), our results align closely with experimental observations, providing a practical and efficient approach for designing metallic or alloy substrates to achieve desired carbon nanostructures and explore further reaction possibilities.

Thermal conductivity of GeTe crystals based on machine learning potentials

GeTe has attracted extensive research interest for thermoelectric applications. In this paper, we first train a neuro-evolution potential (NEP) based on a dataset constructed by ab initio molecular dynamics, with the Gaussian approximation potential (GAP) as a reference. The phonon density of states is then calculated by two machine learning potentials and compared with density functional theory results, with the GAP potential having higher accuracy. Next, the thermal conductivity of a GeTe crystal at 300 K is calculated by the equilibrium molecular dynamics method using both machine learning potentials, and both of them are in good agreement with the experimental results; however, the calculation speed when using the NEP potential is about 500 times faster than when using the GAP potential. Finally, the lattice thermal conductivity in the range of 300 K–600 K is calculated using the NEP potential. The lattice thermal conductivity decreases as the temperature increases due to the phonon anharmonic effect. This study provides a theoretical tool for the study of the thermal conductivity of GeTe.

Interatomic force fields for zirconium based on the embedded atom method and the tabulated Gaussian Approximation Potential

The accuracy of interatomic interaction potentials–also known as force fields–is the main factor determining the physical soundness of classical molecular dynamics (MD) simulations. Here, we present a multi-objective framework to generate embedded-atom-method (EAM) force fields using ab initio data. The EAM force fields were tuned via particle swarm optimization to capture the non-linear association between atomic structures and system energies. Using this framework, 95 standard EAM force fields for zirconium were developed and 45 physical features for each developed force field were tracked. Principal component analysis (PCA) was performed to provide insights into the compromises that must be made when generating EAM force fields. Of note, by assigning large fitting weights to generalized stacking fault energy (GSFE) surfaces, there exist EAM force fields with properly positioned minima on prismatic GSFE surfaces and containing no spurious minima in basal GSFE surfaces. However, while standard EAM force fields achieved this without explicitly taking the angular dependence of atomic interactions into account, they led to a severe mismatch between other important physical properties and benchmarks. Hence, we also constructed two machine-learned tabulated Gaussian approximation potentials (tabGAP) with an additional three-body term, which successfully tackled the aforementioned issue and exhibit acceptable prediction accuracy across many physical properties (lattice parameters, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, and free surface energies) of Zr. Remarkably, its computational efficiency is only 6 times slower than standard EAM force fields.

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.

Gaussian approximation potentials: Theory, software implementation and application examples.

Gaussian Approximation Potentials (GAPs) are a class of Machine Learned Interatomic Potentials routinely used to model materials and molecular systems on the atomic scale. The software implementation provides the means for both fitting models using abinitio data and using the resulting potentials in atomic simulations. Details of the GAP theory, algorithms and software are presented, together with detailed usage examples to help new and existing users. We review some recent developments to the GAP framework, including Message Passing Interface parallelisation of the fitting code enabling its use on thousands of central processing unit cores and compression of descriptors to eliminate the poor scaling with the number of different chemical elements.

Silicon phase transitions in nanoindentation: Advanced molecular dynamics simulations with machine learning phase recognition

Closing the gap between experiments and simulations in the investigation of high-pressure silicon phase transitions calls for advanced, new-generation modeling approaches. By exploiting massive parallelization, we here provide molecular dynamics (MD) simulations of Si nanoindentation based on the Gaussian Approximation Potential (GAP). Results are analyzed by exploiting a customized Neural Network Phase Recognition (NN-PR) approach, helping to shed light on the phase transitions occurring during the simulations. Our results show that GAP provides a realistic description of silicon phase transitions. With the support of NN-PR method, the formation mechanism and stability of high-pressure phases are comprehensively studied. Additionally, we also show how simulations based on the less demanding and widely-used Tersoff potential are still useful to investigate the role played by the indenter tip modeling. However, high-pressure phases obtained with GAP are more consistent with observations made in nanoindentation experiments, removing a spurious phase that is shown by Tersoff simulations. This behavior is explained on the base of relative phase stability with comparison with Density Functional Theory (DFT) calculations. This work provides insight into the application of state-of-the-art Machine Learning (ML) methods on nanoindentation simulations, enabling further understanding of the phase transition mechanisms in silicon.

Global analysis of energy landscapes for materials modeling: A test case for C60.

In this contribution, we employ computational tools from the energy landscape approach to test Gaussian Approximation Potentials (GAPs) for C60. In particular, we apply basin-hopping global optimization and explore the landscape starting from the low-lying minima using discrete path sampling. We exploit existing databases of minima and transition states harvested from previous work using tight-binding potentials. We explore the energy landscape for the full range of structures and pathways spanning from the buckminsterfullerene global minimum up to buckybowls. In the initial GAP model, the fullerene part of the landscape is reproduced quite well. However, there are extensive families of C1@C59 and C2@C58 structures that lie lower in energy. We succeeded in refining the potential to remove these artifacts by simply including two minima from the C2@C58 families found by global landscape exploration. We suggest that the energy landscape approach could be used systematically to test and improve machine learning interatomic potentials.

Comparing interatomic potentials in calculating basic structural parameters and Peierls stress in tungsten-based random binary alloys

The field of machine learning-based interatomic potentials (ML-IAPs) has seen increasing development in recent years. In this work, we compare three widely used ML-IAPs–the moment tensor potential (MTP), the spectral neighbor analysis potential (SNAP), and the tabulated Gaussian approximation potential (tabGAP)with a conventional non-ML-IAP, the embedded atom method (EAM) potential. We evaluated these potentials on the basis of their accuracy and efficiency in determining basic structural parameters and Peierls stress under equivalent conditions. Three tungsten (W)-based alloys (Mo-W, Nb-W, and Ta-W) are considered, and their lattice parameter, formation energy, elastic tensor, and Peierls stress of edge dislocation are calculated. Compared with DFT results, MTP demonstrates the highest accuracy in predicting the lattice parameter and the best computational efficiency among the three ML-IAPs, while tabGAP accurately predicts two independent elastic constants, C 11 and C 12. Despite being the slowest, SNAP shows the highest accuracy in predicting the third independent elastic constant C 44 and its Peierls stress value is comparable to that based on MTP.

Complex Ga2O3 polymorphs explored by accurate and general-purpose machine-learning interatomic potentials

Ga2O3 is a wide-band gap semiconductor of emergent importance for applications in electronics and optoelectronics. However, vital information of the properties of complex coexisting Ga2O3 polymorphs and low-symmetry disordered structures is missing. We develop two types of machine-learning Gaussian approximation potentials (ML-GAPs) for Ga2O3 with high accuracy for β/κ/α/δ/γ polymorphs and generality for disordered stoichiometric structures. We release two versions of interatomic potentials in parallel, namely soapGAP and tabGAP, for high accuracy and exceeding speedup, respectively. Both potentials can reproduce the structural properties of all the five polymorphs in an exceptional agreement with ab initio results, meanwhile boost the computational efficiency with 5 × 102 and 2 × 105 computing speed increases compared to density functional theory, respectively. Moreover, the Ga2O3 liquid-solid phase transition proceeds in three different stages. This experimentally unrevealed complex dynamics can be understood in terms of distinctly different mobilities of O and Ga sublattices in the interfacial layer.

Revisiting four-phonon scattering in WS2 monolayer with machine learning potential

Recently, the importance of the higher-order anharmonic effect on the thermal transport has been demonstrated in a few two-dimensional (2D) materials. As a member of 2D materials, the WS2 monolayer possesses excellent properties, but its higher-order phonon anharmonic effect is still unclear. As an emerging tool for atomistic simulations, the machine learning Gaussian approximation potential (GAP) has good computational speed and accuracy. In this work, the effect of the four-phonon scattering on the thermal transport properties of the WS2 monolayer is systematically investigated by combining a well-trained GAP with the Boltzmann transport equation. We find that the in-plane thermal conductivity of the WS2 monolayer decreases by 34.68% at 300 K compared to the results without considering the four-phonon scattering, which mainly originates from the strong low-frequency redistribution scattering process. The temperature-induced phonon renormalization in WS2 monolayer is investigated using the temperature-dependent effective potential method. The results show that phonon modes slightly soften with increasing temperature, and the temperature effect weakens the four-phonon scattering while hardly affect the three-phonon scattering. Our work reveals that previous studies considering only the three-phonon scattering and the temperature effect are insufficient, and the four-phonon interaction must be introduced to accurately describe the thermal transport properties of the WS2 monolayer.

Multi-reward reinforcement learning based development of inter-atomic potential models for silica

Silica is an abundant and technologically attractive material. Due to the structural complexities of silica polymorphs coupled with subtle differences in Si–O bonding characteristics, the development of accurate models to predict the structure, energetics and properties of silica polymorphs remain challenging. Current models for silica range from computationally efficient Buckingham formalisms (BKS, CHIK, Soules) to reactive (ReaxFF) and more recent machine-learned potentials that are flexible but computationally costly. Here, we introduce an improved formalism and parameterization of BKS model via a multireward reinforcement learning (RL) using an experimental training dataset. Our model concurrently captures the structure, energetics, density, equation of state, and elastic constants of quartz (equilibrium) as well as 20 other metastable silica polymorphs. We also assess its ability in capturing amorphous properties and highlight the limitations of the BKS-type functional forms in simultaneously capturing crystal and amorphous properties. We demonstrate ways to improve model flexibility and introduce a flexible formalism, machine-learned ML-BKS, that outperforms existing empirical models and is on-par with the recently developed 50 to 100 times more expensive Gaussian approximation potential (GAP) in capturing the experimental structure and properties of silica polymorphs and amorphous silica.

AL4GAP: Active learning workflow for generating DFT-SCAN accurate machine-learning potentials for combinatorial molten salt mixtures.

Machine learning interatomic potentials have emerged as a powerful tool for bypassing the spatiotemporal limitations of abinitio simulations, but major challenges remain in their efficient parameterization. We present AL4GAP, an ensemble active learning software workflow for generating multicomposition Gaussian approximation potentials (GAP) for arbitrary molten salt mixtures. The workflow capabilities include: (1) setting up user-defined combinatorial chemical spaces of charge neutral mixtures of arbitrary molten mixtures spanning 11 cations (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba and two heavy species, Nd, and Th) and 4 anions (F, Cl, Br, and I), (2) configurational sampling using low-cost empirical parameterizations, (3) active learning for down-selecting configurational samples for single point density functional theory calculations at the level of Strongly Constrained and Appropriately Normed (SCAN) exchange-correlation functional, and (4) Bayesian optimization for hyperparameter tuning of two-body and many-body GAP models. We apply the AL4GAP workflow to showcase high throughput generation of five independent GAP models for multicomposition binary-mixture melts, each of increasing complexity with respect to charge valency and electronic structure, namely: LiCl-KCl, NaCl-CaCl2, KCl-NdCl3, CaCl2-NdCl3, and KCl-ThCl4. Our results indicate that GAP models can accurately predict structure for diverse molten salt mixture with density functional theory (DFT)-SCAN accuracy, capturing the intermediate range ordering characteristic of the multivalent cationic melts.

Searching for iron nanoparticles with a general-purpose Gaussian approximation potential

We present a general-purpose machine learning Gaussian approximation potential (GAP) for iron that is applicable to all bulk crystal structures found experimentally under diverse thermodynamic conditions, as well as surfaces and nanoparticles (NPs). By studying its phase diagram, we show that our GAP remains stable at extreme conditions, including those found in the Earth's core. The new GAP is particularly accurate for the description of NPs. We use it to identify new low-energy NPs, whose stability is verified by performing density functional theory calculations on the GAP structures. Many of these NPs are lower in energy than those previously available in the literature up to $N_\text{atoms}=100$. We further extend the convex hull of available stable structures to $N_\text{atoms}=200$. For these NPs, we study characteristic surface atomic motifs using data clustering and low-dimensional embedding techniques. With a few exceptions, e.g., at magic numbers $N_\text{atoms}=59$, $65$, $76$ and $78$, we find that iron tends to form irregularly shaped NPs without a dominant surface character or characteristic atomic motif, and no reminiscence of crystalline features. We hypothesize that the observed disorder stems from an intricate balance and competition between the stable bulk motif formation, with bcc structure, and the stable surface motif formation, with fcc structure. We expect these results to improve our understanding of the fundamental properties and structure of low-dimensional forms of iron, and to facilitate future work in the field of iron-based catalysis.

Black box vs gray box: Comparing GAP and GPrep-DFTB for ruthenium and ruthenium oxide.

The increasing popularity of machine learning (ML) approaches in computational modeling, most prominently ML interatomic potentials, opened possibilities that were unthinkable only a few years ago-structure and dynamics for systems up to many thousands of atoms at an abinitio level of accuracy. Strictly referring to ML interatomic potentials, however, a number of modeling applications are out of reach, specifically those that require explicit electronic structure. Hybrid ("gray box") models based on, e.g., approximate, semi-empirical abinitio electronic structure with the aid of some ML components offer a convenient synthesis that allows us to treat all aspects of a certain physical system on the same footing without targeting a separate ML model for each property. Here, we compare one of these [Density Functional Tight Binding with a Gaussian Process Regression repulsive potential (GPrep-DFTB)] with its fully "black box" counterpart, the Gaussian approximation potential, by evaluating performance in terms of accuracy, extrapolation power, and data efficiency for the metallic Ru and oxide RuO2 systems, given exactly the same training set. The accuracy with respect to the training set or similar chemical motifs turns out to be comparable. GPrep-DFTB is, however, slightly more data efficient. The robustness of GPRep-DFTB in terms of extrapolation power is much less clear-cut for the binary system than for the pristine system, most likely due to imperfections in the electronic parametrization.

Effects of lattice and mass mismatch on primary radiation damage in W-Ta and W-Mo binary alloys

The fundamental mechanisms of radiation damage in metal alloys of equiatomic composition are of great research interest due to the possibility to use them as new materials for radiation-hard environments. With W-Ta and W-Mo alloys as examples, this study investigates the effect of two factors, namely the difference in lattice parameters and the difference in masses of the constituent elements, on primary radiation damage by means of atomistic simulations. We compare the trends obtained with the available embedded atom method (EAM) interatomic potential and the tabulated Gaussian approximation potential (tabGAP). We observe a similar trend in the number of surviving defects as a function of alloy composition in W-Mo for both potentials, while the absolute numbers are fairly different. The tabGAP predicts higher resistance to irradiation, i.e. fewer surviving defects after the cascades. On the contrary, the trends of the dependence of surviving defects on alloy composition in W-Ta alloys are very different in the two potentials. We explain this difference by analyzing the threshold displacement energies (TDE) and melting temperatures in these alloys. The mass difference in W-Mo alloys results in Mo atoms with higher TDE in W-Mo alloys. The effect of the lattice parameter mismatch in W-Ta alloys is visible in the change of the number of surviving defects with increase of the W content in W-Ta alloys.