Machine Learning Force Fields Research Articles

Measuring transferability issues in machine-learning force fields: the example of gold–iron interactions with linearized potentials

Machine-learning force fields have been increasingly employed in order to extend the possibility of current first-principles calculations. However, the transferability of the obtained potential cannot always be guaranteed in situations that are outside the original database. To study such limitation, we examined the very difficult case of the interactions in gold–iron nanoparticles. For the machine-learning potential, we employed a linearized formulation that is parameterized using a penalizing regression scheme which allows us to control the complexity of the obtained potential. We showed that while having a more complex potential allows for a better agreement with the training database, it can also lead to overfitting issues and a lower accuracy in untrained systems.

Machine Learning in Computational Surface Science and Catalysis: Case Studies on Water and Metal-Oxide Interfaces.

The goal of many computational physicists and chemists is the ability to bridge the gap between atomistic length scales of about a few multiples of an Ångström (Å), i. e., 10−10 m, and meso- or macroscopic length scales by virtue of simulations. The same applies to timescales. Machine learning techniques appear to bring this goal into reach. This work applies the recently published on-the-fly machine-learned force field techniques using a variant of the Gaussian approximation potentials combined with Bayesian regression and molecular dynamics as efficiently implemented in the Vienna ab initio simulation package, VASP. The generation of these force fields follows active-learning schemes. We apply these force fields to simple oxides such as MgO and more complex reducible oxides such as iron oxide, examine their generalizability, and further increase complexity by studying water adsorption on these metal oxide surfaces. We successfully examined surface properties of pristine and reconstructed MgO and Fe3O4 surfaces. However, the accurate description of water–oxide interfaces by machine-learned force fields, especially for iron oxides, remains a field offering plenty of research opportunities.

Multiple spin-phonon relaxation pathways in a Kramer single-ion magnet.

We present a first-principles investigation of spin-phonon relaxation in a molecular crystal of Co2+ single-ion magnets. Our study combines electronic structure calculations with machine-learning force fields and unravels the nature of both the Orbach and the Raman relaxation channels in terms of atomistic processes. We find that although both mechanisms are mediated by the excited spin states, the low temperature spin dynamics is dominated by phonons in the THz energy range, which partially suppress the benefit of having a large magnetic anisotropy. This study also determines the importance of intra-molecular motions for both the relaxation mechanisms and paves the way to the rational design of a new generation of single-ion magnets with tailored spin-phonon coupling.

A general-purpose machine-learning force field for bulk and nanostructured phosphorus

Elemental phosphorus is attracting growing interest across fundamental and applied fields of research. However, atomistic simulations of phosphorus have remained an outstanding challenge. Here, we show that a universally applicable force field for phosphorus can be created by machine learning (ML) from a suitably chosen ensemble of quantum-mechanical results. Our model is fitted to density-functional theory plus many-body dispersion (DFT + MBD) data; its accuracy is demonstrated for the exfoliation of black and violet phosphorus (yielding monolayers of “phosphorene” and “hittorfene”); its transferability is shown for the transition between the molecular and network liquid phases. An application to a phosphorene nanoribbon on an experimentally relevant length scale exemplifies the power of accurate and flexible ML-driven force fields for next-generation materials modelling. The methodology promises new insights into phosphorus as well as other structurally complex, e.g., layered solids that are relevant in diverse areas of chemistry, physics, and materials science.

Active learning for robust, high-complexity reactive atomistic simulations

Machine learned reactive force fields based on polynomial expansions have been shown to be highly effective for describing simulations involving reactive materials. Nevertheless, the highly flexible nature of these models can give rise to a large number of candidate parameters for complicated systems. In these cases, reliable parameterization requires a well-formed training set, which can be difficult to achieve through standard iterative fitting methods. Here, we present an active learning approach based on cluster analysis and inspired by Shannon information theory to enable semi-automated generation of informative training sets and robust machine learned force fields. The use of this tool is demonstrated for development of a model based on linear combinations of Chebyshev polynomials explicitly describing up to four-body interactions, for a chemically and structurally diverse system of C/O under extreme conditions. We show that this flexible training database management approach enables development of models exhibiting excellent agreement with Kohn-Sham density functional theory in terms of structure, dynamics, and speciation.

Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields.

Modern machine learning force fields (ML-FF) are able to yield energy and force predictions at the accuracy of high-level ab initio methods, but at a much lower computational cost. On the other hand, classical molecular mechanics force fields (MM-FF) employ fixed functional forms and tend to be less accurate, but considerably faster and transferable between molecules of the same class. In this work, we investigate how both approaches can complement each other. We contrast the ability of ML-FF for reconstructing dynamic and thermodynamic observables to MM-FFs in order to gain a qualitative understanding of the differences between the two approaches. This analysis enables us to modify the generalized AMBER force field by reparametrizing short-range and bonded interactions with more expressive terms to make them more accurate, without sacrificing the key properties that make MM-FFs so successful.

Liquid to crystal Si growth simulation using machine learning force field

Machine learning force field (ML-FF) has emerged as a potential promising approach to simulate various material phenomena for large systems with ab initio accuracy. However, most ML-FFs have been used to study the phenomena relatively close to the equilibrium ground states. In this work, we have studied a far from equilibrium system of liquid to crystal Si growth using ML-FF. We found that our ML-FF based on ab initio decomposed atomic energy can reproduce all the aspects of ab initio simulated growth, from local energy fluctuations to transition temperatures, to diffusion constant, and growth rates. We have also compared the growth simulation with the Stillinger-Weber classical force field and found significant differences. A procedure is also provided to correct a systematic fitting bias in the ML-FF training process, which exists in all training models, otherwise critical results like transition temperature will be wrong.

Neural network potential from bispectrum components: A case study on crystalline silicon.

In this article, we present a systematic study on developing machine learning force fields (MLFFs) for crystalline silicon. While the main-stream approach of fitting a MLFF is to use a small and localized training set from molecular dynamics simulations, it is unlikely to cover the global features of the potential energy surface. To remedy this issue, we used randomly generated symmetrical crystal structures to train a more general Si-MLFF. Furthermore, we performed substantial benchmarks among different choices of material descriptors and regression techniques on two different sets of silicon data. Our results show that neural network potential fitting with bispectrum coefficients as descriptors is a feasible method for obtaining accurate and transferable MLFFs.

On-the-Fly Active Learning of Interatomic Potentials for Large-Scale Atomistic Simulations.

The on-the-fly generation of machine-learning force fields by active-learning schemes attracts a great deal of attention in the community of atomistic simulations. The algorithms allow the machine to self-learn an interatomic potential and construct machine-learned models on the fly during simulations. State-of-the-art query strategies allow the machine to judge whether new structures are out of the training data set or not. Only when the machine judges the necessity of updating the data set with the new structures are first-principles calculations carried out. Otherwise, the yet available machine-learned model is used to update the atomic positions. In this manner, most of the first-principles calculations are bypassed during training, and overall, simulations are accelerated by several orders of magnitude while retaining almost first-principles accuracy. In this Perspective, after describing essential components of the active-learning algorithms, we demonstrate the power of the schemes by presenting recent applications.

Machine Learning and Reactive Force Field Molecular Dynamics Investigation of Electrolytes for Ultra-fast Charging Li-ion Batteries

The ultra-fast charging batteries have become a bigger demand for electric vehicles. To achieve the fast charging system, the electrolyte system should be optimized with a high balance between ionic conductivity and chemical stability. In recent research, many compounds, including organic ester, formate, and nitrile, were introduced into carbonate-based electrolytes as a co-solvent. However, the understanding of how co-solvents and effect of functional groups improve the electrolyte properties is not yet disclosed. Here we investigate the role of co-solvent that affects electrolyte properties, especially the self-diffusion coefficient by using theoretical reactive molecular dynamics (RMDs) simulations coupled with the advancement in numerical method to compute the correlation between co-solvent properties and the self-diffusion coefficient. We found that the low electron affinity co-solvent and low-density molecule are the keys to improve the Li-ion diffusion in the carbonate-based electrolyte system. Hence, this work could lead the way for developing the new co-solvent for the ultra-fast charging demand.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems.

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

An On-the-Fly Approach to Construct Generalized Energy-Based Fragmentation Machine Learning Force Fields of Complex Systems.

An on-the-fly fragment-based machine learning (ML) approach was developed to construct machine learning force fields for large complex systems. In this approach, the energy, forces, and molecular properties of the target system are obtained by combining machine learning force fields of various subsystems with the generalized energy-based fragmentation (GEBF) approach. Using a nonparametric Gaussian process (GP) model, all the force fields of subsystems are automatically generated online without data selection and parameter optimization. With the GEBF-ML force field constructed for a normal alkane, C60H122, long-time molecular dynamics (MD) simulations are performed on different sizes of alkanes, and the predicted energy, forces, and molecular properties (dipole moment) are favorably comparable with full quantum mechanics (QM) calculations. The predicted IR spectra also show excellent agreement with the direct ab initio MD results. Our results demonstrate that the GEBF-ML method provides an automatic and efficient way to build force fields for a broad range of complex systems such as biomolecules and supramolecular systems.

On-the-fly active learning of interpretable Bayesian force fields for atomistic rare events

Machine learned force fields typically require manual construction of training sets consisting of thousands of first principles calculations, which can result in low training efficiency and unpredictable errors when applied to structures not represented in the training set of the model. This severely limits the practical application of these models in systems with dynamics governed by important rare events, such as chemical reactions and diffusion. We present an adaptive Bayesian inference method for automating the training of interpretable, low-dimensional, and multi-element interatomic force fields using structures drawn on the fly from molecular dynamics simulations. Within an active learning framework, the internal uncertainty of a Gaussian process regression model is used to decide whether to accept the model prediction or to perform a first principles calculation to augment the training set of the model. The method is applied to a range of single- and multi-element systems and shown to achieve a favorable balance of accuracy and computational efficiency, while requiring a minimal amount of ab initio training data. We provide a fully open-source implementation of our method, as well as a procedure to map trained models to computationally efficient tabulated force fields.

Making free-energy calculations routine: Combining first principles with machine learning

The chemical potentials of atoms and molecules in condensed matter are fundamental properties that allow one to predict a wide variety of thermodynamic properties. However, predictions using first principles are challenging. Here, an efficient and accurate method using machine-learned force fields is presented. A key point is that it requires training only at the end points of the thermodynamic pathway, rendering the training simple and efficient. Applications to liquid Si, and Li and F ions hydrated by water show that the method can predict accurate chemical potentials at low computational cost.

Pushing the limits of atomistic simulations towards ultra-high temperature: A machine-learning force field for ZrB2

Determining thermal and physical quantities across a broad temperature domain, especially up to the ultra-high temperature region, is a formidable theoretical and experimental challenge. At the same time it is essential for understanding the performance of ultra-high temperature ceramic (UHTC) materials. Here we present the development of a machine-learning force field for ZrB2, one of the primary members of the UHTC family with a complex bonding structure. The force field exhibits chemistry accuracy for both energies and forces and can reproduce structural, elastic and phonon properties, including thermal expansion and thermal transport. A thorough comparison with available empirical potentials shows that our force field outperforms the competitors with the merits of high accuracy and great versatility. Most importantly, its effectiveness is extended from room temperature to the ultra-high temperature region (up to ∼ 2500 K), where measurements are very difficult, costly and some time impossible. Our work demonstrates that machine-learning force fields (MLFF) can be used for simulations of materials in a harsh environment, where no experimental tools are available, but crucial for a number of engineering applications, such as in aerospace, aviation and nuclear.

Efficient sampling of high-energy states by machine learning force fields.

Regarding their application in the field of molecular sciences, machine learning (ML) methods are capable of combining the high accuracy of ab initio potentials with an efficiency closer to that of classical molecular mechanics. By relying on the reference data (e.g., atomic configurations and corresponding energies), the ML algorithms can reconstruct the potential energy surface for simple molecular systems, which may subsequently serve as a computationally inexpensive force field. The accuracy of such an ML force field is highly dependent on the character of the dataset that was used for its training. In this work, we show that omitting the high-energy states, which results from following the Boltzmann distribution, may lead to a catastrophic loss of accuracy in certain regions of the configurational phase space. To overcome this challenge, we have proposed an alternative solution for generating the ML input data. The most essential step is the biased subsampling of the configurations, aimed at increasing the population of hardly accessible states, usually located on energy barriers. The applicability of the proposed procedure is demonstrated on the example of conformational rearrangements in the two flexible, heterocyclic molecules. This approach provides an essential component required to obtain the ML force fields, accurate within the whole configurational phase space of the system.

Toward ab Initio Ground States of Gold Clusters via Neural Network Modeling

Prescreening candidate structures with reliable classical potentials is an effective way to accelerate ab initio ground state searches. Given the growing popularity of machine learning force fields...

Phase diagram of uranium fromab initiocalculations and machine learning

Experimental studies of materials at extreme conditions are challenging, and as a consequence, P-T phase diagrams are still unknown for many elements and materials. In this work, we present the P-T phase diagram of uranium calculated up to extreme conditions. First, we searched for possible crystal structures using the evolutionary algorithm USPEX. Their free energies were then calculated using thermodynamic integration (TI) and temperature-dependent effective potential techniques. TI was performed using molecular dynamics, employing a machine learning (ML) force field trained on energies and forces from density-functional calculations at the generalized gradient approximation level. The prediction error of the ML force field for the energy was less than 10 meV/atom. Using thermodynamic perturbation theory (including first and second order corrections), from the free energies of the ML force field, we obtained free energies and phase diagram at the level of quality of the underlying density-functional calculations at pressures up to 800 GPa and temperatures up to 16 000 K.

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.