Publisher Correction: Fine-Tuning Universal Machine-Learned Interatomic Potentials for Applications in the Science of Steels

Simulation studies of the stability and growth kinetics of Pt-Sn phases using a machine learning interatomic potential

Machine learning (ML) interatomic potentials (ML-IAPs) are generated for alkane and polyene hydrocarbons using on-the-fly adaptive sampling and a sparse Gaussian process regression (SGPR) algorithm. The ML model is generated based on the PBE+D3 level of density functional theory (DFT) with molecular dynamics (MD) for small alkane and polyene molecules. Intermolecular interactions are also trained with clusters and condensed phases of small molecules. It shows excellent transferability to long alkanes and closely describes the ab inito potential energy surface for polyenes. Simulation of liquid ethane also shows reasonable agreement with experimental reports. This is a promising initiative toward a universal ab initio quality force-field for hydrocarbons and organic molecules.

Spline-based neural network interatomic potentials: Blending classical and machine learning models

Foundational machine-learning interatomic potentials (MLIPs) are being developed at a rapid pace, promising closer and closer approximation to abinitio accuracy. This unlocks the possibility to simulate much larger length and time scales. However, benchmarks for these MLIPs are usually limited to ordered, crystalline, and bulk materials. Hence, reported performance does not necessarily reflect MLIP performance accurately in real applications such as heterogeneous catalysis. Here, we systematically analyze zero-shot performance of 80 different MLIPs, evaluating tasks typical for heterogeneous catalysis across a range of different datasets, including adsorption and reaction on surfaces of alloyed metals, oxides, and metal-oxide interfacial systems. We demonstrate that current-generation foundational MLIPs can already perform with high accuracy for applications such as predicting vacancy formation energies of perovskite oxides or zero-point energies of supported nanoclusters. However, limitations also exist. We find that many MLIPs catastrophically fail when applied to magnetic materials, and structure relaxation in the MLIP generally increases the energy prediction error compared to single-point evaluation of a previously optimized structure. Comparing low-cost, task-specific models to foundational MLIPs, we highlight some core differences between these model approaches and show that-if considering only accuracy-these models can compete with the current generation of best-performing MLIPs. Furthermore, we show that no single MLIP universally performs best, requiring users to investigate MLIP suitability for their desired application.

The promise of machine learning interatomic potentials (MLIPs) has led to an abundance of public quantum mechanical (QM) training datasets. The quality of an MLIP is directly limited by the accuracy of the energies and atomic forces in the training dataset. Unfortunately, most of these datasets are computed with relatively low-accuracy QM methods, e.g. density functional theory with a moderate basis set. Due to the increased computational cost of more accurate QM methods, e.g. coupled-cluster theory with a complete basis set (CBS) extrapolation, most high-accuracy datasets are much smaller and often do not contain atomic forces. The lack of high-accuracy atomic forces is quite troubling, as training with force data greatly improves the stability and quality of the MLIP compared to training to energy alone. Because most datasets are computed with a unique level of theory, traditional single-fidelity (SF) learning is not capable of leveraging the vast amounts of published QM data. In this study, we apply multi-fidelity learning (MFL) to train an MLIP to multiple QM datasets of different levels of accuracy, i.e. levels of fidelity. Specifically, we perform three test cases to demonstrate that MFL with both low-level forces and high-level energies yields an extremely accurate MLIP—far more accurate than a SF MLIP trained solely to high-level energies and almost as accurate as a SF MLIP trained directly to high-level energies and forces. Therefore, MFL greatly alleviates the need for generating large and expensive datasets containing high-accuracy atomic forces and allows for more effective training to existing high-accuracy energy-only datasets. Indeed, low-accuracy atomic forces and high-accuracy energies are all that are needed to achieve a high-accuracy MLIP with MFL.

Niobium (Nb) and its alloys are extensively used in various technological applications owing to their favorable mechanical, thermal and irradiation properties. Accurately modeling Nb under irradiation is essential for predicting microstructural changes, defect evolution, and overall material performance. Many classical interatomic potentials for Nb have found difficulty in predicting the correct self-interstitial atom (SIA) configuration, a critical factor in radiation damage simulations. We develop a machine learning interatomic potential (MLIP) within the spectral neighbor analysis potential (SNAP) framework. The potential was trained on a high-fidelity dataset generated from ab initio density functional theory (DFT) calculations. This dataset was refined using diversity-based selection algorithms, and the MLIP was developed through cross-validation combined with multivariate hyperparameter optimization. The developed MLIP accurately captures a wide range of material properties, particularly the non-equilibrium properties crucial for radiation damage simulations, such as threshold displacement energies, relative stabilities of various SIA configurations, edge dislocation loop stability, and close pair-potential interactions. The resulting MLIP reproduces DFT-level accuracy while maintaining computational efficiency for large-scale molecular dynamics (MD) simulations. Through a series of validation tests involving elastic, thermal, and defect properties—including high energy collision cascade simulations—we show that our SNAP potential performs very well for radiation damage studies, and resolves persistent limitations present in earlier embedded atom method and Finnis–Sinclair potentials. It shows competitive advantage in accuracy and efficiency aspects compared to other MLIP and modern semi-empirical potential. Using detailed statistical results of dumbbell orientations formed in collision cascades carried out using the developed MLIP and three other interatomic potentials, we show the differences in formation energies have drastic effect on the defect configurations at primary damage produced in a collision cascade. Our developed potential accurately captures the relative stability of all defect configurations of Nb, its threshold displacement energy and other equilibrium properties offering a robust tool for predictive irradiation studies.

Machine learning approaches have recently emerged as powerful tools to probe structure-property relationships in crystals and molecules. Specifically, machine learning interatomic potentials (MLIPs) can accurately reproduce first-principles data at a cost similar to that of conventional interatomic potential approaches. While MLIPs have been extensively tested across various classes of materials and molecules, a clear characterization of the anharmonic terms encoded in the MLIPs is lacking. Here, we benchmark popular MLIPs using the anharmonic vibrational Hamiltonian of ThO2 in the fluorite crystal structure, which was constructed from density functional theory (DFT) using our highly accurate and efficient irreducible derivative methods. The anharmonic Hamiltonian was used to generate molecular dynamics (MD) trajectories, which were used to train three classes of MLIPs: Gaussian approximation potentials, artificial neural networks (ANN), and graph neural networks (GNN). The results were assessed by directly comparing phonons and their interactions, as well as phonon linewidths, phonon lineshifts, and thermal conductivity. The models were also trained on a DFT MD dataset, demonstrating good agreement up to fifth-order for the ANN and GNN. Our analysis demonstrates that MLIPs have great potential for accurately characterizing anharmonicity in materials systems at a fraction of the cost of conventional first principles-based approaches.

The marriage of ab initio calculations and machine learning (ML) methods exhibits bright application prospects in interatomic potential development. In this work, a concurrent learning scheme is implemented to automatically generate ML interatomic potential for the MgCl2‐NaCl eutectic. This scheme allows to train ML interatomic potential with training datasets approximately four times smaller than that of previous work, which significantly reduces the computational cost. The learned ML interatomic potential is used to accelerate the ab initio estimation of the properties of MgCl2‐NaCl eutectic, thermal conductivity in particular. With the learned models, simulations are conducted on multiple system sizes (1464–4392 atoms) and a wide temperature range (773–1073 K). The impact of the finite‐size effect on simulated thermal conductivity and derived size‐independent thermal conductivity is carefully investigated. The simulated thermal conductivities decrease with temperature and are in the range 0.469–0.538 W m−1 K−1 at 773–1073 K, which is in reasonable agreement with the literature data. Overall, the training scheme and the learned potential have produced reliable and satisfactory results, and promise to open up new avenues in the computational modeling of molten salts.

Thermo-mechanical properties of nitrogenated holey graphene (C2N): A comparison of machine-learning-based and classical interatomic potentials

Since the birth of the concept of machine learning interatomic potentials (MLIPs) in 2007, a growing interest has been developed in the replacement of empirical interatomic potentials (EIPs) with MLIPs, in order to conduct more accurate and reliable molecular dynamics calculations. As an exciting novel progress, in the last couple of years the applications of MLIPs have been extended towards the analysis of mechanical and failure responses, providing novel opportunities not heretofore efficiently achievable, neither by EIPs nor by density functional theory (DFT) calculations. In this minireview, we first briefly discuss the basic concepts of MLIPs and outline popular strategies for developing a MLIP. Next, by considering several examples of recent studies, the robustness of MLIPs in the analysis of the mechanical properties will be highlighted, and their advantages over EIP and DFT methods will be emphasized. MLIPs furthermore offer astonishing capabilities to combine the robustness of the DFT method with continuum mechanics, enabling the first-principles multiscale modeling of mechanical properties of nanostructures at the continuum level. Last but not least, the common challenges of MLIP-based molecular dynamics simulations of mechanical properties are outlined and suggestions for future investigations are proposed.

Machine learning interatomic potentials (MLIPs) are a promising technique for atomic modeling. While small errors are widely reported for MLIPs, an open concern is whether MLIPs can accurately reproduce atomistic dynamics and related physical properties in molecular dynamics (MD) simulations. In this study, we examine the state-of-the-art MLIPs and uncover several discrepancies related to atom dynamics, defects, and rare events (REs), compared to ab initio methods. We find that low averaged errors by current MLIP testing are insufficient, and develop quantitative metrics that better indicate the accurate prediction of atomic dynamics by MLIPs. The MLIPs optimized by the RE-based evaluation metrics are demonstrated to have improved prediction in multiple properties. The identified errors, the evaluation metrics, and the proposed process of developing such metrics are general to MLIPs, thus providing valuable guidance for future testing and improvements of accurate and reliable MLIPs for atomistic modeling.

We introduce a machine-learning (ML) interatomic potential for Mg-H system based on Behler-Parrinello approach. In order to fit the complex bonding conditions in the cluster structure, we combine multiple sampling strategies to obtain training samples that contain a variety of local atomic environments. First-principles calculations based on density functional theory (DFT) are employed to get reference energies and forces for training the ML potential. For the calculation of bulk properties, phonon dispersion, gas-phase ${\mathrm{H}}_{2}$ interactions, and the potential energy surface (PES) for ${\mathrm{H}}_{2}$ dissociative adsorption on Mg(0001) surfaces, our ML potential has reached DFT accuracy at the level of GGA-PBE, and can be extended by combining the DFT-D3 method to describe van der Waals interaction. Moreover, through molecular dynamics (MD) simulations based on the ML potential, we find that for ${\mathrm{Mg}}_{n}{\mathrm{H}}_{m}$ clusters, $\mathrm{Mg}/\mathrm{Mg}{\mathrm{H}}_{x}$ phase separation occurs when $ml2n$, and for a cluster with a diameter of about 4 nm, the Mg part of the cluster forms a hexagonal close-packed (hcp) nanocrystalline structure at low temperature. Also, the calculated diffusion coefficients reproduce the experimental values and confirm an Arrhenius type temperature dependence in the range of 400 to 700 K.

Machine learning interatomic potentials (MLIPs) have massively changed the field of atomistic modeling. They enable the accuracy of density functional theory in large-scale simulations while being nearly as fast as classical interatomic potentials. Over the last few years, a wide range of different types of MLIPs have been developed, but it is often difficult to judge which approach is the best for a given problem setting. For the case of structurally and chemically complex solids, namely Al-Cu-Zr and Si-O, we benchmark a range of machine learning interatomic potential approaches, in particular, the Gaussian approximation potential (GAP), high-dimensional neural network potentials (HDNNP), moment tensor potentials (MTP), the atomic cluster expansion (ACE) in its linear and nonlinear version, neural equivariant interatomic potentials (NequIP), Allegro, and MACE. We find that nonlinear ACE and the equivariant, message-passing
graph neural networks NequIP and MACE form the Pareto front in the accuracy vs. computational cost trade-off. In case of the Al-Cu-Zr system we find that MACE and Allegro offer the highest accuracy, while NequIP outperforms them for Si-O. Furthermore, GPUs can massively accelerate the MLIPs, bringing them on par with and even ahead of non-accelerated classical interatomic potentials (IPs) with regards to accessible timescales. Finally, we explore the extrapolation behavior of the corresponding potentials, probe the smoothness of the potential energy surfaces, and finally estimate the user friendliness of the corresponding fitting codes and molecular dynamics interfaces.

We present machine‐learning interatomic potentials (MLIPs) for simulations of Si–C–O–H compounds. The MLIPs are constructed from moment tensor potentials (MTPs) and were trained to a library of configurations that included polysiloxane structures, hypothetical crystalline and amorphous SiCOH structures, and trajectories of Si–C–O–H systems obtained via ab initio molecular dynamic (aiMD) simulations at elevated temperatures. Passive, active, and hybrid learning strategies were implemented to develop the MLIPs. The MLIPs reproduce vibrational properties of polymers and SiCOH structures obtained from aiMD simulations, thus providing a tool to identify chemical units and distinct structural characteristics through their vibrational properties. Simulations of the polymer‐to‐ceramic transformation show the development of mixed tetrahedra in SiCO ceramics and align with experimental observations. Million‐atom simulations for several nanoseconds highlight the precipitation of graphitic nanosheets from a carbon‐rich SiCO precursor. Atomistic simulations with the MLIPs deliver details of chemical reaction mechanisms during the pyrolysis of polysiloxanes, including methane abstraction and Kumada‐like rearrangements that transform the siloxane backbone. While the MLIPs still leave room for systematic improvement, they deliver simulations with “density functional theory (DFT)‐like” quality at low and high temperatures.

The emergence of artificial intelligence is profoundly impacting computational chemistry, particularly through machine-learning interatomic potentials (MLIPs). Unlike traditional potential energy surface representations, MLIPs overcome the conventional computational scaling limitations by offering an effective combination of accuracy and efficiency for calculating atomic energies and forces to be used in molecular simulations. These MLIPs have significantly enhanced molecular simulations across various applications, including large-scale simulations of materials, interfaces, chemical reactions, and beyond. Despite these advances, the construction of training datasets-a critical component for the accuracy of MLIPs-has not received proportional attention, especially in the context of chemical reactivity, which depends on rare barrier-crossing events that are not easily included in the datasets. Here we address this gap by introducing ArcaNN, a comprehensive framework designed for generating training datasets for reactive MLIPs. ArcaNN employs a concurrent learning approach combined with advanced sampling techniques to ensure an accurate representation of high-energy geometries. The framework integrates automated processes for iterative training, exploration, new configuration selection, and energy and force labeling, all while ensuring reproducibility and documentation. We demonstrate ArcaNN's capabilities through two paradigm reactions: a nucleophilic substitution and a Diels-Alder reaction. These examples showcase its effectiveness, the uniformly low error of the resulting MLIP everywhere along the chemical reaction coordinate, and its potential for broad applications in reactive molecular dynamics. Finally, we provide guidelines for assessing the quality of MLIPs in reactive systems.