Machine Learning Force Research Articles

FFLUX molecular simulations driven by atomic Gaussian process regression models.

Machine learning (ML) force fields are revolutionizing molecular dynamics (MD) simulations as they bypass the computational cost associated with ab initio methods but do not sacrifice accuracy in the process. In this work, the GPyTorch library is used to create Gaussian process regression (GPR) models that are interfaced with the next-generation ML force field FFLUX. These models predict atomic properties of different molecular configurations that appear in a progressing MD simulation. An improved kernel function is utilized to correctly capture the periodicity of the input descriptors. The first FFLUX molecular simulations of ammonia, methanol, and malondialdehyde with the updated kernel are performed. Geometry optimizations with the GPR models result in highly accurate final structures with a maximum root-mean-squared deviation of 0.064 Å and sub-kJ mol-1 total energy predictions. Additionally, the models are tested in 298 K MD simulations with FFLUX to benchmark for robustness. The resulting energy and force predictions throughout the simulation are in excellent agreement with ab initio data for ammonia and methanol but decrease in quality for malondialdehyde due to the increased system complexity. GPR model improvements are discussed, which will ensure the future scalability to larger systems.

Parameter-Free and Electron Counting Satisfied Material Representation for Machine Learning Potential Energy and Force Fields.

We proposed a parameter-free volume element representation that satisfies the electron counting model and obtains accurate machine learning potential energy and direct force fitting of randomly perturbed hexagonal BN. Our method preserves permutational, translational, and rotational invariance and can be extended to three-dimensional systems, verified by a system of bulk Si. As a result, we obtained 0.57 meV/atom potential energy root mean squared error (RMSE) and 59 meV/Å force RMSE for perturbed bulk BN systems and 0.43 meV/atom potential energy RMSE and 36 meV/Å force RMSE for perturbed Si systems. In addition, an unbiased perturbation-based data set construction scheme is introduced and a continuous population distribution is obtained with a training data set of 4500, which is about 1 order of magnitude smaller than standard methods based on first-principles molecular dynamics simulations and saves a large amount of computing resources. General validity of our model is verified by structure optimization, molecular dynamics simulations, and extrapolations.

How close are the classical two-body potentials to abinitio calculations? Insights from linear machine learning based force matching.

In this work, we propose a linear machine learning force matching approach that can directly extract pair atomic interactions from abinitio calculations in amorphous structures. The local feature representation is specifically chosen to make the linear weights a force field as a force/potential function of the atom pair distance. Consequently, this set of functions is the closest representation of the abinitio forces, given the two-body approximation and finite scanning in the configurational space. We validate this approach in amorphous silica. Potentials in the new force field (consisting of tabulated Si-Si, Si-O, and O-O potentials) are significantly different than existing potentials that are commonly used for silica, even though all of them produce the tetrahedral network structure and roughly similar glass properties. This suggests that the commonly used classical force fields do not offer fundamentally accurate representations of the atomic interaction in silica. The new force field furthermore produces a lower glass transition temperature (Tg ∼ 1800K) and a positive liquid thermal expansion coefficient, suggesting the extraordinarily high Tg and negative liquid thermal expansion of simulated silica could be artifacts of previously developed classical potentials. Overall, the proposed approach provides a fundamental yet intuitive way to evaluate two-body potentials against abinitio calculations, thereby offering an efficient way to guide the development of classical force fields.

Atomic diffusion in liquid gallium and gallium-nickel alloys probed by quasielastic neutron scattering and molecular dynamic simulations

The atomic mobility in liquid pure gallium and a gallium-nickel alloy with 2 at% of nickel is studied experimentally by incoherent quasielastic neutron scattering. The integral diffusion coefficients for all-atom diffusion are derived from the experimental data at different temperatures. DFT-based ab-initio molecular dynamics (MD) is used to find numerically the diffusion coefficient of liquid gallium at different temperatures, and numerical theory results well agree with the experimental findings at temperatures below 500 K. Machine learning force fields derived from ab-initio molecular dynamics (AIMD) overestimate within a small 6% error the diffusion coefficient of pure gallium within the genuine AIMD. However, they better agree with experiment for pure gallium and enable the numerical finding of the diffusion coefficient of nickel in the considered melted alloy along with the diffusion coefficient of gallium and integral diffusion coefficient, that agrees with the corresponding experimental values within the error bars. The temperature dependence of the gallium diffusion coefficient DGa(T) follows the Arrhenius law experimentally for all studied temperatures and below 500 K also in the numerical simulations. However, DGa(T) can be well described alternatively by an Einstein–Stokes dependence with the metallic liquid viscosity following the Arrhenius law, especially for the MD simulation results at all studied temperatures. Moreover, a novel variant of the excess entropy scaling theory rationalized our findings for gallium diffusion. Obtained values of the Arrhenius activation energies are profoundly different in the competing theoretical descriptions, which is explained by different temperature-dependent prefactors in the corresponding theories. The diffusion coefficient of gallium is significantly reduced (at the same temperature) in a melted alloy with natural nickel, even at a tiny 2 at% concentration of nickel, as compared with its pure gallium value. This highly surprising behavior contradicts the existing excess entropy scaling theories and opens a venue for further research.

Development of machine learning force field for thermal conductivity analysis in MoAlB: Insights into anisotropic heat transfer mechanisms

The MAB phases have garnered significant attention as a new generation high-temperature structural materials due to their outstanding high-temperature mechanical properties, resistance to oxidation at elevated temperatures, low-temperature synthesis, and machining capabilities. The chemically anisotropic bonding within MAB phases leads to unique anisotropic elastic properties, oxidation behavior, and electrical characteristics, posing challenges in understanding the structure-property relationships.To address this challenge, we leveraged recent advances in machine learning force fields based on quantum mechanics methods. Using ab initio molecular dynamics simulations, we constructed a comprehensive dataset and developed an accurate machine learning force field for the Mo–Cr–Al–B system based on deep neural network. We then employed non-equilibrium molecular dynamics simulations to calculate the phonon thermal conductivity of MoAlB, investigating its temperature dependence and anisotropy. Our analysis includes phonon density of states, phonon participation ratio, and spectral heat flux analysis, shedding light on the temperature-dependent anisotropy of phonon thermal conductivity in MoAlB. This work not only provides a reliable force field for large-scale molecular dynamics simulations but also advances our understanding of the composition-structure-performance relationship in MAB phases.

Molecular Gas-Phase Conformational Ensembles.

Accurately determining the global minima of a molecular structure is important in diverse scientific fields, including drug design, materials science, and chemical synthesis. Conformational search engines serve as valuable tools for exploring the extensive conformational space of molecules and for identifying energetically favorable conformations. In this study, we present a comparison of Auto3D, CREST, Balloon, and ETKDG (from RDKit), which are freely available conformational search engines, to evaluate their effectiveness in locating global minima. These engines employ distinct methodologies, including machine learning (ML) potential-based, semiempirical, and force field-based approaches. To validate these methods, we propose the use of collisional cross-section (CCS) values obtained from ion mobility-mass spectrometry studies. We hypothesize that experimental gas-phase CCS values can provide experimental evidence that we likely have the global minimum for a given molecule. To facilitate this effort, we used our gas-phase conformation library (GPCL) which currently consists of the full ensembles of 20 small molecules and can be used by the community to validate any conformational search engine. Further members of the GPCL can be readily created for any molecule of interest using our standard workflow used to compute CCS values, expanding the ability of the GPCL in validation exercises. These innovative validation techniques enhance our understanding of the conformational landscape and provide valuable insights into the performance of conformational generation engines. Our findings shed light on the strengths and limitations of each search engine, enabling informed decisions for their utilization in various scientific fields, where accurate molecular structure determination is crucial for understanding biological activity and designing targeted interventions. By facilitating the identification of reliable conformations, this study significantly contributes to enhancing the efficiency and accuracy of molecular structure determination, with particular focus on metabolite structure elucidation. The findings of this research also provide valuable insights for developing effective workflows for predicting the structures of unknown compounds with high precision.

First principles molecular dynamics simulation and thermal decomposition kinetics study of CL-20.

2,4,6,8,10, 12-hexanitro-2,4,6,8,10, 12-hexazepane (CL-20) is a new energetic material with high performance and low sensitivity. In-depth study of the thermal decomposition mechanism of CL-20 is a necessary condition to improve its performance, ensure its safety, and optimize its application. On the basis of a large number of empirical force fields used in molecular dynamics simulation in the past, the machine learning augmented first-principles molecular dynamics method was used for the first time to simulate the thermal decomposition reaction of CL-20 at 2200 K, 2500 K, 2800 K, and 3000 K isothermal temperature. The main stable resulting compounds are N2, CO2, CO, H2O, andH2, where CO2 and H2O continue to decompose at higher temperatures. The initial decomposition pathways are denitration by N-N fracture, ring-opening by C-N bond fracture, and redox reaction involving NO2 and CL-20. After ring opening, two main compounds, fused tricyclic pyrazine and azadicyclic, were formed, which were decomposed continuously to form monocyclic pyrazine and pyrazole ring structures. The most common fragments formed during decomposition are those containing two, three, four, and six carbons. The formation rule and quantity of main small molecule intermediates and resulting stable products under different simulated temperatures were analyzed. Based on ab initio Bayesian active learning algorithm, efficient and accurate prediction of CL-20 is made using the dynamic machine learning function of Vienna Ab-Initio Simulation Package (VASP), which constructs the energy potential surface by learning a large number of data based on AIMD calculations. The result is a machine learning force field (MLFF). Then the molecular dynamics of CL-20 was simulated using the trained MLFF model. PAW pseudopotentials and generalized gradient approximation (GGA), namely, Perdew-Burke-Ernzerhof (PBE) functional, are used in the calculation. The plane wave truncation energy (ENCUT) is set to 550 eV, and using the Gaussian broadening, the thermal broadening size of the single-electron orbital is 0.05 eV. A van der Waals revision of the system with Grimme Version 3. The energy convergence accuracy (EDIFF) of electron self-consistent iteration is set to 1E-5 eV and 1E-6 eV, respectively. The two-step structure optimization is carried out using 1'1'1 k point grid and conjugate gradient method. The ENCUT was changed to 500 eV and EDIFF to 1E-5 eV, and NVT integration (ISIF = 2) of Langevin thermostat was used for machine learning force field training and AIMD simulation of the system.

A Machine Learning Force Field for Bio-Macromolecular Modeling Based on Quantum Chemistry-Calculated Interaction Energy Datasets.

Accurate energy data from noncovalent interactions are essential for constructing force fields for molecular dynamics simulations of bio-macromolecular systems. There are two important practical issues in the construction of a reliable force field with the hope of balancing the desired chemical accuracy and working efficiency. One is to determine a suitable quantum chemistry level of theory for calculating interaction energies. The other is to use a suitable continuous energy function to model the quantum chemical energy data. For the first issue, we have recently calculated the intermolecular interaction energies using the SAPT0 level of theory, and we have systematically organized these energies into the ab initio SOFG-31 (homodimer) and SOFG-31-heterodimer datasets. In this work, we re-calculate these interaction energies by using the more advanced SAPT2 level of theory with a wider series of basis sets. Our purpose is to determine the SAPT level of theory proper for interaction energies with respect to the CCSD(T)/CBS benchmark chemical accuracy. Next, to utilize these energy datasets, we employ one of the well-developed machine learning techniques, called the CLIFF scheme, to construct a general-purpose force field for biomolecular dynamics simulations. Here we use the SOFG-31 dataset and the SOFG-31-heterodimer dataset as the training and test sets, respectively. Our results demonstrate that using the CLIFF scheme can reproduce a diverse range of dimeric interaction energy patterns with only a small training set. The overall errors for each SAPT energy component, as well as the SAPT total energy, are all well below the desired chemical accuracy of ~1 kcal/mol.

The emergence of machine learning force fields in drug design.

In the field of molecular simulation for drug design, traditional molecular mechanic force fields and quantum chemical theories have been instrumental but limited in terms of scalability and computational efficiency. To overcome these limitations, machine learning force fields (MLFFs) have emerged as a powerful tool capable of balancing accuracy with efficiency. MLFFs rely on the relationship between molecular structures and potential energy, bypassing the need for a preconceived notion of interaction representations. Their accuracy depends on the machine learning models used, and the quality and volume of training data sets. With recent advances in equivariant neural networks and high-quality datasets, MLFFs have significantly improved their performance. This review explores MLFFs, emphasizing their potential in drug design. It elucidates MLFF principles, provides development and validation guidelines, and highlights successful MLFF implementations. It also addresses potential challenges in developing and applying MLFFs. The review concludes by illuminating the path ahead for MLFFs, outlining the challenges to be overcome and the opportunities to be harnessed. This inspires researchers to embrace MLFFs in their investigations as a new tool to perform molecular simulations in drug design.

Hydrogen diffusion in zirconium hydrides from on-the-fly machine learning molecular dynamics

Reactor pressure vessels and fuel cladding tubes have repeatedly failed due to zirconium hydrides. Zirconium hydride precipitation and growth are directly affected by hydrogen atom transport properties, which would make nuclear fuel storage less safe over long periods of time. Herein, we employ first-principles calculations to investigate the hydrogen diffusion mechanism in zirconium hydrides, utilizing on-the-fly machine learning force field molecular dynamics. It is verified that the machine learning force field can accurately describe the hydrogen atomic diffusion properties in zirconium hydrides at several temperatures and compositions. The atomic migration paths of hydrogen in zirconium hydrides as well as their barriers and pre-factors are also calculated. According to our results, the temperature and composition of zirconium hydrides affect the microscopic dynamical behavior of hydrogen.

Machine learning molecular dynamics simulations of liquid methanol

As the simplest hydrogen-bonded alcohol, liquid methanol has attracted intensive experimental and theoretical interest. However, theoretical investigations on this system have primarily relied on empirical intermolecular force fields or ab initio molecular dynamics with semilocal density functionals. Inspired by recent studies on bulk water using increasingly accurate machine learning force fields, we report a new machine learning force field for liquid methanol with a hybrid functional revPBE0 plus dispersion correction. Molecular dynamics simulations on this machine learning force field are orders of magnitude faster than ab initio molecular dynamics simulations, yielding the radial distribution functions, self-diffusion coefficients, and hydrogen bond network properties with very small statistical errors. The resulting structural and dynamical properties are compared well with the experimental data, demonstrating the superior accuracy of this machine learning force field. This work represents a successful step toward a first-principles description of this benchmark system and showcases the general applicability of the machine learning force field in studying liquid systems.

Stability and transferability of machine learning force fields for molecular dynamics applications

We benchmark GNN models for MLFF-MD and introduce new metrics beyond conventional force and energy errors. Our approach, demonstrated on lithium-ion conductors, aims to broaden ionic conductor screening for batteries.

Computational prediction of solvation structures in calcium battery electrolytes

This study demonstrates comprehensive approaches for predicting solvation structures in Ca-ion battery electrolytes by integrating ab initio calculations and machine learning force fields.

Tracking Li atoms in real-time with ultra-fast NMR simulations.

We present for the first time a multiscale machine learning approach to jointly simulate atomic structure and dynamics with the corresponding solid state Nuclear Magnetic Resonance (ssNMR) observables. We study the use-case of spin-alignment echo (SAE) NMR for exploring Li-ion diffusion within the solid state electrolyte material Li3PS4 (LPS) by calculating quadrupolar frequencies of 7Li. SAE NMR probes long-range dynamics down to microsecond-timescale hopping processes. Therefore only a few machine learning force field schemes are able to capture the time- and length scales required for accurate comparison with experimental results. By using a new class of machine learning interatomic potentials, known as ultra-fast potentials (UFPs), we are able to efficiently access timescales beyond the microsecond regime. In tandem, we have developed a machine learning model for predicting the full 7Li electric field gradient (EFG) tensors in LPS. By combining the long timescale trajectories from the UFP with our model for 7Li EFG tensors, we are able to extract the autocorrelation function (ACF) for 7Li quadrupolar frequencies during Li diffusion. We extract the decay constants from the ACF for both crystalline β-LPS and amorphous LPS, and find that the predicted Li hopping rates are on the same order of magnitude as those predicted from the Li dynamics. This demonstrates the potential for machine learning to finally make predictions on experimentally relevant timescales and temperatures, and opens a new avenue of NMR crystallography: using machine learning dynamical NMR simulations for accessing polycrystalline and glass ceramic materials.

Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields.

The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.

Force Field Analysis Software and Tools (FFAST): Assessing Machine Learning Force Fields under the Microscope.

As the sophistication of machine learning force fields (MLFF) increases to match the complexity of extended molecules and materials, so does the need for tools to properly analyze and assess the practical performance of MLFFs. To go beyond average error metrics and into a complete picture of a model's applicability and limitations, we developed FFAST (force field analysis software and tools): a cross-platform software package designed to gain detailed insights into a model's performance and limitations, complete with an easy-to-use graphical user interface. The software allows the user to gauge the performance of any molecular force field,─such as popular state-of-the-art MLFF models, ─ on various popular data set types, providing general prediction error overviews, outlier detection mechanisms, atom-projected errors, and more. It has a 3D visualizer to find and picture problematic configurations, atoms, or clusters in a large data set. In this paper, the example of the MACE and NequIP models is used on two data sets of interest [stachyose and docosahexaenoic acid (DHA)]─to illustrate the use cases of the software. With this, it was found that carbons and oxygens involved in or near glycosidic bonds inside the stachyose molecule present increased prediction errors. In addition, prediction errors on DHA rise as the molecule folds, especially for the carboxylic group at the edge of the molecule. We emphasize the need for a systematic assessment of MLFF models for ensuring their successful application to the study of dynamics of molecules and materials.

Calibration of uncertainty in the active learning of machine learning force fields

FFLUX is a machine learning force field that uses the maximum expected prediction error (MEPE) active learning algorithm to improve the efficiency of model training. MEPE uses the predictive uncertainty of a Gaussian process (GP) to balance exploration and exploitation when selecting the next training sample. However, the predictive uncertainty of a GP is unlikely to be accurate or precise immediately after training. We hypothesize that calibrating the uncertainty quantification within MEPE will improve active learning performance. We develop and test two methods to improve uncertainty estimates: post-hoc calibration of predictive uncertainty using the CRUDE algorithm, and replacing the GP with a student-t process. We investigate the impact of these methods on MEPE for single sample and batch sample active learning. Our findings suggest that post-hoc calibration does not improve the performance of active learning using the MEPE method. However, we do find that the student-t process can outperform active learning strategies and random sampling using a GP if the training set is sufficiently large.

Machine-learning-driven simulations on microstructure, thermodynamic properties, and transport properties of LiCl-KCl-LiF molten salt

The thermodynamic and transport properties of high-temperature chloride molten salt systems are of great significance for spent fuel reprocessing in the field of nuclear energy engineering. Here, by using machine learning based deep potential (DP) method, we train a high-precision force field model for the LiCl-KCl-LiF system. During force field training, adding new dataset through multiple iterations improves the accuracy of the force field model and its applicability to more configurations. The comparison of density functional theory (DFT) and DP results for the test dataset indicates that our trained DP model has the same accuracy as DFT. Then, we comprehensively investigate the local structure, thermophysical properties, and transport properties of the LiCl-KCl and LiCl-KCl-LiF molten salt systems using the trained DP model. The effects of temperature and LiF concentration on the above properties are analyzed. This work provides guidance for the training of machine learning force fields in molten salt systems and the study of basic physical properties of high-temperature chloride molten salt systems.

Physics infused machine learning force fields for 2D materials monolayers

Large-scale atomistic simulations of two-dimensional (2D) materials rely on highly accurate and efficient force fields. Here, we present a physics-infused machine learning framework that enables the efficient development and interpretability of interatomic interaction models for 2D materials. By considering the characteristics of chemical bonds and structural topology, we have devised a set of efficient descriptors. This enables accurate force field training using a small dataset. The machine learning force fields show great success in describing the phase transformation and domain switching behaviors of monolayer Group IV monochalcogenides, e.g., GeSe and PbTe. Notably, this type of force field can be readily extended to other non-transition 2D systems, such as hexagonal boron nitride (h BN), leveraging their structural similarity. Our work provides a straightforward but accurate extension of simulation time and length scales for 2D materials.

Modelling electrified microporous carbon/electrolyte electrochemical interface and unraveling charge storage mechanism by machine learning accelerated molecular dynamics

Ion storage in electric double layer (EDL) of microporous carbon (< 1 nm) has been demonstrated to be a partially desolvated structure, leading to a capacitance increase. Due to the relevance of the interface structure to capacitance behavior and charge storage mechanism, it is critical to give a deep insight into the micropore/electrolyte interface at the molecular scale. Ab initio molecular dynamics (AIMD) simulation can describe the electronic structure and dynamic properties of the EDL. However, the complex EDL is hard to be well equilibrated at the limited time scale of the AIMD simulation. Here, we have performed machine learning force field accelerated molecular dynamics (MLMD) to construct the EDL of microporous carbon at different electrode potentials with a much lower cost while keeping ab initio accuracy. Based on the MLMD with a longer time scale, we have clarified the microscopic information of the interface, such as the distributions of ions and water molecules. By simulating the Na+ intercalation process, the critical role of the electrode potential on ion storage in pore is clarified. In addition, according to the MLMD simulation on micropore/electrolyte EDLs with different pore sizes, the pore size of ∼0.65 nm is appropriate for desolvation effect due to the match between the pore size and the solvated ion size. These theoretical results provide a way for studying micropore/electrolyte EDL by MLMD and improving the electrochemical performance of microporous carbon electrodes.