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

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

Accurate and Transferable Machine Learning Potential for Molecular Dynamics Simulation of Sodium Silicate Glasses

An accurate and transferable machine learning (ML) potential for the simulation of binary sodium silicate glasses over a wide range of compositions (from 0 to 50% Na2O) was developed. The potential energy surface is approximated by the sum of atomic energy contributions mapped by a neural network algorithm from the local geometry comprising information on atomic distances and angles with neighboring atoms using the DeePMD code [Wang, H. Comput. Phys. Commun. 2018, 228, 178-184]. Our model was trained on a large data set of total energies and atomic forces computed at the density functional theory level on structures extracted from classical molecular dynamics (MD) simulations performed at several temperatures from 300 to 3000 K. This allows for the generation of a robust and transferable ML potential applicable over the full compositional range of glass formability at different temperatures that outperforms the empirical potentials available in the literature in reproducing structures and properties such as bond angle distribution, total distribution functions, and vibrational density of state. The generality of the approach enables the future training of a potential with other or more elements allowing for simulations of structures, properties, and behavior of ternary and multicomponent oxide glasses with nearly ab initio accuracy at a fraction of the computational cost.

Machine learning molecular dynamics reveals the structural origin of the first sharp diffraction peak in high-density silica glasses

The first sharp diffraction peak (FSDP) in the total structure factor has long been regarded as a characteristic feature of medium-range order (MRO) in amorphous materials with a polyhedron network, and its underlying structural origin is a subject of ongoing debate. In this study, we utilized machine learning molecular dynamics (MLMD) simulations to explore the origin of FSDP in two typical high-density silica glasses: silica glass under pressure and permanently densified glass. Our MLMD simulations accurately reproduce the structural properties of high-density silica glasses observed in experiments, including changes in the FSDP intensity depending on the compression temperature. By analyzing the simulated silica glass structures, we uncover the structural origin responsible for the changes in the MRO at high density in terms of the periodicity between the ring centers and the shape of the rings. The reduction or enhancement of MRO in the high-density silica glasses can be attributed to how the rings deform under compression.

Determination of hyper-parameters in the atomic descriptors for efficient and robust molecular dynamics simulations with machine learning forces

The atomic descriptors used in machine learning to predict forces are often high dimensional. In general, by retrieving a significant amount of structural information from these descriptors, accurate force predictions can be achieved. On the other hand, to acquire higher robustness for transferability without overfitting, sufficient reduction of descriptors should be necessary. In this study, we propose a method to automatically determine hyperparameters in the atomic descriptors, aiming to obtain accurate machine learning forces while using a small number of descriptors. Our method focuses on identifying an appropriate threshold cut-off for the variance value of the descriptor components. To demonstrate the effectiveness of our method, we apply it to crystalline, liquid, and amorphous structures in SiO₂, SiGe, and Si systems. By using both conventional two-body descriptors and our introduced split-type three-body descriptors, we demonstrate that our method can provide machine learning forces that enable efficient and robust molecular dynamics simulations.

Self-learning hybrid Monte Carlo method for isothermal-isobaric ensemble: Application to liquid silica

Self-learning hybrid Monte Carlo (SLHMC) is a first-principles simulation that allows for exact ensemble generation on potential energy surfaces based on density functional theory. The statistical sampling can be accelerated with the assistance of smart trial moves by machine learning potentials. In the first report [Nagai et al., Phys. Rev. B 102, 041124(R) (2020)], the SLHMC approach was introduced for the simplest case of canonical sampling. We herein extend this idea to isothermal-isobaric ensembles to enable general applications for soft materials and liquids with large volume fluctuation. As a demonstration, the isothermal-isobaric SLHMC method was used to study the vibrational structure of liquid silica at temperatures close to the melting point, whereby the slow diffusive motion is beyond the time scale of first-principles molecular dynamics. It was found that the static structure factor thus computed from first-principles agrees quite well with the high-energy x-ray data.

Strategies for the construction of machine-learning potentials for accurate and efficient atomic-scale simulations

Recent advances in machine-learning interatomic potentials have enabled the efficient modeling of complex atomistic systems with an accuracy that is comparable to that of conventional quantum-mechanics based methods. At the same time, the construction of new machine-learning potentials can seem a daunting task, as it involves data-science techniques that are not yet common in chemistry and materials science. Here, we provide a tutorial-style overview of strategies and best practices for the construction of artificial neural network (ANN) potentials. We illustrate the most important aspects of (a) data collection, (b) model selection, (c) training and validation, and (d) testing and refinement of ANN potentials on the basis of practical examples. Current research in the areas of active learning and delta learning are also discussed in the context of ANN potentials. This tutorial review aims at equipping computational chemists and materials scientists with the required background knowledge for ANN potential construction and application, with the intention to accelerate the adoption of the method, so that it can facilitate exciting research that would otherwise be challenging with conventional strategies.

Modeling microsolvation clusters with electronic-structure calculations guided by analytical potentials and predictive machine learning techniques

We propose a new methodology to study, at the density functional theory (DFT) level, the clusters resulting from the microsolvation of alkali-metal ions with rare-gas atoms. The workflow begins with a global optimization search to generate a pool of low-energy minimum structures for different cluster sizes. This is achieved by employing an analytical potential energy surface (PES) and an evolutionary algorithm (EA). The next main stage of the methodology is devoted to establish an adequate DFT approach to treat the microsolvation system, through a systematic benchmark study involving several combinations of functionals and basis sets, in order to characterize the global minimum structures of the smaller clusters. In the next stage, we apply machine learning (ML) classification algorithms to predict how the low-energy minima of the analytical PES map to the DFT ones. An early and accurate detection of likely DFT local minima is extremely important to guide the choice of the most promising low-energy minima of large clusters to be re-optimized at the DFT level of theory. In this work, the methodology was applied to the Li+Krn (n = 2-14 and 16) microsolvation clusters for which the most competitive DFT approach was found to be the B3LYP-D3/aug-pcseg-1. Additionally, the ML classifier was able to accurately predict most of the solutions to be re-optimized at the DFT level of theory, thereby greatly enhancing the efficiency of the process and allowing its applicability to larger clusters.

Effects of density and composition on the properties of amorphous alumina: A high-dimensional neural network potential study

Amorphous alumina (a-AlO_x), which plays important roles in several technological fields, shows a wide variation of density and composition. However, their influences on the properties of a-AlO_x have rarely been investigated from a theoretical perspective. In this study, high-dimensional neural network potentials were constructed to generate a series of atomic structures of a-AlO_x with different densities (2.6 g/cm³-3.3 g/cm³) and O/Al ratios (1.0-1.75). The structural, vibrational, mechanical, and thermal properties of the a-AlO_x models were investigated, as well as the Li and Cu diffusion behavior in the models. The results showed that density and composition had different degrees of effects on the different properties. The structural and vibrational properties were strongly affected by composition, whereas the mechanical properties were mainly determined by density. The thermal conductivity was affected by both the density and composition of a-AlO_x. However, the effects on the Li and Cu diffusion behavior were relatively unclear.

Recursive evaluation and iterative contraction of N-body equivariant features

Mapping an atomistic configuration to a symmetrized N-point correlation of a field associated with the atomic positions (e.g., an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible N-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different order (generalizations of N-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically improvable, symmetry adapted representations for atomistic machine learning.