Machine Learning Force Fields Research Articles

Long-range order imposed by short-range interactions in methylammonium lead iodide: Comparing point-dipole models to machine-learning force fields

The crystal structure of the ${\mathrm{MAPbI}}_{3}$ hybrid perovskite forms an intricate electrostatic puzzle with different ordering patterns of the MA molecules at elevated temperatures. For this perovskite three published model Hamiltonians based on the point-dipole (pd) approximation combined with short-range effective interactions are compared to a recently developed machine-learning force field. A molecular order parameter is used to consistently compare the transformation of the antiferroelectric ordering in the orthorhombic phase upon raising the temperature. We show that the ground states and the order-disorder transition of the three models are completely different. Our analysis indicates that the long-range order in the low-temperature orthorhombic phase can be captured by pd-based models with a short cutoff radius, including the nearest and next-nearest neighbor molecules. By constructing effective atomic interactions the ordering can already be described within a 6 \AA{} radius. By extracting the coupling energetics of the molecules from density functional theory calculations on ${\mathrm{MA}}_{x}{\mathrm{Cs}}_{1\ensuremath{-}x}{\mathrm{PbI}}_{3}$ test systems, we show that the pd approximation holds at least for static structures. To improve the accuracy of the pd interaction an Ewald summation is applied combined with a distance dependent electronic screening function.

Toward Fast and Reliable Potential Energy Surfaces for Metallic Pt Clusters by Hierarchical Delta Neural Networks.

Data-driven machine learning force fields (MLFs) are more and more popular in atomistic simulations and exploit machine learning methods to predict energies and forces for unknown structures based on the knowledge learned from an existing reference database. The latter usually comes from density functional theory calculations. One main drawback of MLFs is that physical laws are not incorporated in the machine learning models, and instead, MLFs are designed to be very flexible to simulate complex quantum chemistry potential energy surface (PES). In general, MLFs have poor transferability, and hence, a very large trainset is required to span all the target feature space to get a reliable MLF. This procedure becomes more troublesome when the PES is complicated, with a large number of degrees of freedom, in which building a large database is inevitable and very expensive, especially when accurate but costly exchange-correlation functionals have to be used. In this manuscript, we exploit a high-dimensional neural network potential (HDNNP) on Pt clusters of sizes from 6 to 20 as one example. Our standard level of energy calculation is DFT GGA (PBE) using a plane wave basis set. We introduce an approximate but fast level with the PBE functional and a minimal atomic orbital basis set, and then, a more accurate but expensive level, using a hybrid functional or nonlocal vdW functional and a plane wave basis set, is reliably predicted by learning the difference with HDNNP. The results show that such a differential approach (named ΔHDNNP) can deliver very accurate predictions (error <10 meV/atom) in reference to converged basis set energies as well as more accurate but expensive xc functionals. The overall speedup can be as large as 900 for a 20 atom Pt cluster. More importantly, ΔHDNNP shows much better transferability due to the intrinsic smoothness of the delta potential energy surface, and accordingly, one can use much smaller trainset data to obtain better accuracy than the conventional HDNNP. A multilayer ΔHDNNP is thus proposed to obtain very accurate predictions versus expensive nonlocal vdW functional calculations in which the required trainset is further reduced. The approach can be easily generalized to any other machine learning methods and opens a path to study the structure and dynamics of Pt clusters and nanoparticles.

Iterative-Learning Strategy for the Development of Application-Specific Atomistic Force Fields

Emerging data-driven approaches in materials science have triggered the development of numerous machine-learning force fields. In practice, they are constructed by training a statistical model on a reference database to predict potential energy and/or atomic forces. Although most of the force fields can accurately recover the properties of the training set, some of them are becoming useful for actual molecular dynamics simulations. In this work, we employ a simple iterative-learning strategy for the development of machine-learning force fields targeted at specific simulations (applications). The strategy involves (1) preparing and fingerprinting a diverse reference database of atomic configurations and forces, (2) generating a pool of machine-learning force fields by learning the reference data, (3) validating the force fields against a series of targeted applications, and (4) selectively and recursively improving the force fields that are unsuitable for a given application while keeping their performance...

On-the-fly machine learning force field generation: Application to melting points

An efficient and robust on-the-fly machine learning force field method is developed and integrated into an electronic-structure code. This method realizes automatic generation of machine learning force fields on the basis of Bayesian inference during molecular dynamics simulations, where the first principles calculations are only executed, when new configurations out of already sampled datasets appear. The developed method is applied to the calculation of melting points of Al, Si, Ge, Sn and MgO. The applications indicate that more than 99 \% of the first principles calculations are bypassed during the force field generation. This allows the machine to quickly construct first principles datasets over wide phase spaces. Furthermore, with the help of the generated machine learning force fields, simulations are accelerated by a factor of thousand compared with first principles calculations. Accuracies of the melting points calculated by the force fields are examined by thermodynamic perturbation theory, and the examination indicates that the machine learning force fields can quantitatively reproduce the first principles melting points.

Phase Transitions of Hybrid Perovskites Simulated by Machine-Learning Force Fields Trained on the Fly with Bayesian Inference.

Realistic finite temperature simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of computing time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during molecular dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chemical precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multielement complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temperatures of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.

Towards exact molecular dynamics simulations with machine-learned force fields

Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as good as the underlying interatomic potential. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. Here we enable the direct construction of flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model in an automatic data-driven way. The developed sGDML approach faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged molecular dynamics simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations.

Building machine learning force fields for nanoclusters.

We assess Gaussian process (GP) regression as a technique to model interatomic forces in metal nanoclusters by analyzing the performance of 2-body, 3-body, and many-body kernel functions on a set of 19-atom Ni cluster structures. We find that 2-body GP kernels fail to provide faithful force estimates, despite succeeding in bulk Ni systems. However, both 3- and many-body kernels predict forces within an ∼0.1 eV/Å average error even for small training datasets and achieve high accuracy even on out-of-sample, high temperature structures. While training and testing on the same structure always provide satisfactory accuracy, cross-testing on dissimilar structures leads to higher prediction errors, posing an extrapolation problem. This can be cured using heterogeneous training on databases that contain more than one structure, which results in a good trade-off between versatility and overall accuracy. Starting from a 3-body kernel trained this way, we build an efficient non-parametric 3-body force field that allows accurate prediction of structural properties at finite temperatures, following a newly developed scheme [A. Glielmo et al., Phys. Rev. B 95, 214302 (2017)]. We use this to assess the thermal stability of Ni19 nanoclusters at a fractional cost of full ab initio calculations.

Comparison of different machine learning models for the prediction of forces in copper and silicon dioxide.

Recently, the machine learning (ML) force field has emerged as a powerful atomic simulation approach because of its high accuracy and low computational cost. However, there have been relatively fewer applications to multicomponent materials. In this study, we construct and compare ML force fields for both an elemental material (Cu) and binary material (SiO2) with varied inputs and regression models. The atomic environments are described by structural fingerprints that take into account the bond angle, and then, different ML techniques, including linear regression, a neural network and a mixture model method, are used to learn the structure-force relationship. We found that using angular structural fingerprints and a mixture model method significantly improves the accuracy of ML force fields. Additionally, we discuss an effective structural fingerprint auto-selection method based on the least absolute shrinkage and selection operator and the genetic algorithm. The atomic simulations conducted for ML force fields are in excellent agreement with ab initio calculations. As a result of the simulation with our ML force field for the structural and vibrational properties of amorphous SiO2, simulated annealing with a slow cooling rate improved the ring statistics in the amorphous structure and the phonon density of states.

A universal strategy for the creation of machine learning-based atomistic force fields

Emerging machine learning (ML)-based approaches provide powerful and novel tools to study a variety of physical and chemical problems. In this contribution, we outline a universal strategy to create ML-based atomistic force fields, which can be used to perform high-fidelity molecular dynamics simulations. This scheme involves (1) preparing a big reference dataset of atomic environments and forces with sufficiently low noise, e.g., using density functional theory or higher-level methods, (2) utilizing a generalizable class of structural fingerprints for representing atomic environments, (3) optimally selecting diverse and non-redundant training datasets from the reference data, and (4) proposing various learning approaches to predict atomic forces directly (and rapidly) from atomic configurations. From the atomistic forces, accurate potential energies can then be obtained by appropriate integration along a reaction coordinate or along a molecular dynamics trajectory. Based on this strategy, we have created model ML force fields for six elemental bulk solids, including Al, Cu, Ti, W, Si, and C, and show that all of them can reach chemical accuracy. The proposed procedure is general and universal, in that it can potentially be used to generate ML force fields for any material using the same unified workflow with little human intervention. Moreover, the force fields can be systematically improved by adding new training data progressively to represent atomic environments not encountered previously.

Energy-free machine learning force field for aluminum

We used the machine learning technique of Li et al. (PRL 114, 2015) for molecular dynamics simulations. Atomic configurations were described by feature matrix based on internal vectors, and linear regression was used as a learning technique. We implemented this approach in the LAMMPS code. The method was applied to crystalline and liquid aluminum and uranium at different temperatures and densities, and showed the highest accuracy among different published potentials. Phonon density of states, entropy and melting temperature of aluminum were calculated using this machine learning potential. The results are in excellent agreement with experimental data and results of full ab initio calculations.

A study of adatom ripening on an Al (1 1 1) surface with machine learning force fields

Surface phenomena are increasingly becoming important in exploring nanoscale materials growth and characterization. Consequently, the need for atomistic based simulations is increasing. Recently, we proposed a machine learning approach, known as AGNI, that allows fast and quantum mechanical accurate atomic force predictions given an atom’s neighborhood environment. Here, we make use of such force fields to study and characterize the nanoscale diffusion and growth processes occurring on an Al (111) surface. In particular we focus on the adatom ripening phenomena, confirming past experimental findings, wherein a low and high temperature growth regime were observed using entirely molecular dynamics simulations.

Machine Learning Force Fields: Construction, Validation, and Outlook

Force fields developed with machine learning methods in tandem with quantum mechanics are beginning to find merit, given their (i) low cost, (ii) accuracy, and (iii) versatility. Recently, we proposed one such approach, wherein, the vectorial force on an atom is computed directly from its environment. Here, we discuss the multistep workflow required for their construction, which begins with generating diverse reference atomic environments and force data, choosing a numerical representation for the atomic environments, down selecting a representative training set, and lastly the learning method itself, for the case of Al. The constructed force field is then validated by simulating complex materials phenomena such as surface melting and stress–strain behavior, that truly go beyond the realm of ab initio methods, both in length and time scales. To make such force fields truly versatile an attempt to estimate the uncertainty in force predictions is put forth, allowing one to identify areas of poor performance...