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Modeling Equilibrium Solid–Liquid Interfaces under Effective Constant Chemical Potential Using Machine Learning Interatomic Potentials

The chemical potential (μ) of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot maintain constant chemical potential with reference to a targeted concentration or chemical potential under nonequilibrium or dynamic conditions, as solute species can migrate to the interface and deplete (or enrich) the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative quasi-constant chemical potential molecular dynamics (iqCμMD) simulation, which helps simulate targeted molar concentrations of species in solution. iqCμMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target bulk concentration (chemical potential), which allows simulation of the interface under the bulk conditions comparable to experiment. We demonstrate our approach using machine learning interatomic potential (MLIP)-based MD simulations of the Na 2 SO 4,aq –graphene interface, and to show the transferability of our approach, we also perform classical force field-based MD simulations of NaCl aq –air and NaCl aq –graphite interfaces, which produce comparable results to previous CμMD simulations. Our results also show that the iqCμMD approach efficiently achieves the desired bulk ion concentration within two iterations, and by utilizing MLIPs, we can achieve converged results using relatively small-scale simulations compared to previous CμMD simulations. By combining iqCμMD with MLIP-driven simulations, solid–liquid interfaces can be modeled under an effective constant chemical potential with DFT-level accuracy. Here, we show that iqCμMD offers a robust and simple computational framework for constant chemical potential simulations, as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Chemical structure

Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials

Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.

97 MATHEMATICS AND COMPUTING

The transformative capability of quantum-accurate machine learning interatomic potentials

Many materials’ properties and phase boundaries are generally not well known under extreme pressure and temperature conditions. Here, this is a consequence of the scarcity of experimental information and the difficulty of extrapolating approximations to the atomic interactions in such conditions. Nguyen-Cong and colleagues, in their publication (J.Phys.Chem.Lett. 15, 1152 (2024)) [1], achieved an impressive result using a SNAP (Spectral Neighbor Analysis Potential), an interatomic potential for carbon obtained by machine learning techniques. In a way, their contribution closes a full circle of research that spanned more than three decades.

Tedesco, Alfredo Correa [Lawrence Livermore Nation

Systematic softening in universal machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) have introduced a new paradigm for atomic simulations. Recent advancements have led to universal MLIPs (uMLIPs) that are pre-trained on diverse datasets, providing opportunities for universal force fields and foundational machine learning models. However, their performance in extrapolating to out-of-distribution complex atomic environments remains unclear. In this study, we highlight a consistent potential energy surface (PES) softening effect in three uMLIPs: M3GNet, CHGNet, and MACE-MP-0, which is characterized by energy and force underprediction in atomic-modeling benchmarks including surfaces, defects, solid-solution energetics, ion migration barriers, phonon vibration modes, and general high-energy states. The PES softening behavior originates primarily from the systematically underpredicted PES curvature, which derives from the biased sampling of near-equilibrium atomic arrangements in uMLIP pre-training datasets. Our findings suggest that a considerable fraction of uMLIP errors are highly systematic, and can therefore be efficiently corrected. We argue for the importance of a comprehensive materials dataset with improved PES sampling for next-generation foundational MLIPs.

36 MATERIALS SCIENCE

Teacher-student training improves the accuracy and efficiency of machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) are revolutionizing the field of molecular dynamics (MD) simulations. Recent MLIPs have tended towards more complex architectures trained on larger datasets. The resulting increase in computational and memory costs may prohibit the application of these MLIPs to perform large-scale MD simulations. Herein, we present a teacher-student training framework in which the latent knowledge from the teacher (atomic energies) is used to augment the students' training. We show that the light-weight student MLIPs have faster MD speeds at a fraction of the memory footprint compared to the teacher models. Remarkably, the student models can even surpass the accuracy of the teachers, even though both are trained on the same quantum chemistry dataset. Our work highlights a practical method for MLIPs to reduce the resources required for large-scale MD simulations.

36 MATERIALS SCIENCE

Full-stack Quantification of Variability in Predicting Ion Transport Properties using Machine-learned Interatomic Potentials

Machine-learned interatomic potentials (MLIPs) have become the state-of-the-art for performing accurate, scalable molecular dynamics (MD) simulations. It is therefore crucial to understand and quantify the reliability of MLIPs for downstream property predictions. Uncertainty in predicted properties can arise from limitations in first-principles training data, intrinsic MLIP model errors in representing the data, and the statistical noise introduced during subsequent MD simulations. Using ion transport in Li7P3S11 as a case study, we systematically assess the impact of training set size and selection, neural network stochasticity, and MD sampling statistics on predicted diffusivity and activation energy. We find that when using equivariant MLIP architectures with standard MD protocols, uncertainty arising from MD sampling dominates over model-induced errors. In contrast, MLIP errors relative to the underlying first-principles data are consistently minor. Given this, there are two main routes to improving the accuracy of predictions based on MLIP potentials: adopting higher accuracy reference data generation methods, and improving the MD sampling statistics.

36 MATERIALS SCIENCE

Integrating machine learning interatomic potentials with hybrid reverse Monte Carlo structure refinements in RMCProfile

Structure refinement with reverse Monte Carlo (RMC) is a powerful tool for interpreting experimental diffraction data. To ensure that the under-constrained RMC algorithm yields reasonable results, the hybrid RMC approach applies interatomic potentials to obtain solutions that are both physically sensible and in agreement with experiment. To expand the range of materials that can be studied with hybrid RMC, we have implemented a new interatomic potential constraint in RMCProfile that grants flexibility to apply potentials supported by the Large-scale Atomic/Molecular Massively Parallel Simulator ( LAMMPS ) molecular dynamics code. This includes machine learning interatomic potentials, which provide a pathway to applying hybrid RMC to materials without currently available interatomic potentials. To this end, we present a methodology to use RMC to train machine learning interatomic potentials for hybrid RMC applications.

Cuillier, Paul

Predicting Melt Properties Using Atomistic Simulations With A Highly Accurate Physically Informed Neural Network Interatomic Potential

The use of a recently developed machine learning (ML) interatomic potential for molecular dynamics simulations of aluminum melt properties will be presented. Such properties are critical for process modeling in additive manufacturing, including the melt pool size, solidification, and formation of solidification microstructures. Direct first-principles modeling of these processes is computationally prohibitive whereas simulations employing ML potentials combine the high accuracy of quantum-mechanical methods with high computational speeds. The physically-informed neural network (PINN) method used herein, integrates a high-dimensional regression implemented by an artificial neural network with a physics-based bond-order interatomic potential. PINN potentials can accurately reproduce many properties of aluminum in both crystalline-solid and liquid phases. We examine the accuracy of a PINN Al potential in predicting the density, self-diffusivity, viscosity, and the tension of the liquid surface and liquid-solid interfaces. Comparison with experimental data and ab initio molecular dynamics calculations shows very good agreement for all properties tested.

molecular dynamics

A Universal Augmentation Framework for Long-Range Electrostatics in Machine Learning Interatomic Potentials

Most current machine learning interatomic potentials (MLIPs) rely on short-range approximations, without explicit treatment of long-range electrostatics. To address this, we recently developed the Latent Ewald Summation (LES) method, which infers electrostatic interactions, polarization, and Born effective charges (BECs), just by learning from energy and force training data. Here, in this study, we present LES as a standalone library, compatible with any short-range MLIP, and demonstrate its integration with methods such as MACE, NequIP, Allegro, CACE, CHGNet, and UMA. We benchmark LES-enhanced models on distinct systems, including bulk water, polar dipeptides, and gold dimer adsorption on defective substrates, and show that LES not only captures correct electrostatics but also improves accuracy. Additionally, we scale LES to large and chemically diverse data by training MACELES-OFF on the SPICE set containing molecules and clusters, making a universal MLIP with electrostatics for organic systems, including biomolecules. MACELES-OFF is more accurate than its short-range counterpart (MACE-OFF) trained on the same data set, predicts dipoles and BECs reliably, and has better descriptions of bulk liquids. By enabling efficient long-range electrostatics without directly training on electrical properties, LES paves the way for electrostatic foundation MLIPs.

Kim, Dongjin [University of California, Berkeley,

Accuracy, transferability, and computational efficiency of interatomic potentials for simulations of carbon under extreme conditions

Large-scale atomistic molecular dynamics (MD) simulations provide an exceptional opportunity to advance the fundamental understanding of carbon under extreme conditions of high pressures and temperatures. However, the fidelity of these simulations depends heavily on the accuracy of classical interatomic potentials governing the dynamics of many-atom systems. Here, this study critically assesses several popular empirical potentials for carbon, as well as machine learning interatomic potentials (MLIPs), in their ability to simulate a range of physical properties at high pressures and temperatures, including the diamond equation of state, its melting line, shock Hugoniot, uniaxial compressions, and the structure of liquid carbon. Empirical potentials fail to accurately predict the behavior of carbon under high pressure–temperature conditions. In contrast, MLIPs demonstrate quantum accuracy, with Spectral Neighbor Analysis Potential (SNAP) and atomic cluster expansion (ACE) being the most accurate in reproducing the density functional theory results. ACE displays remarkable transferability despite not being specifically trained for extreme conditions. Furthermore, ACE and SNAP exhibit superior computational performance on graphics processing unit-based systems in billion atom MD simulations, with SNAP emerging as the fastest. In addition to offering practical guidance in selecting an interatomic potential with a fine balance of accuracy, transferability, and computational efficiency, this work also highlights transformative opportunities for groundbreaking scientific discoveries facilitated by quantum-accurate MD simulations with MLIPs on emerging exascale supercomputers.

36 MATERIALS SCIENCE

The structure and migration of twin boundaries in tetragonal β -Sn: An application of machine learning based interatomic potentials

Although atomistic simulations have contributed significantly to our understanding of twin boundary structure and migration in metals and alloys with hexagonal close packed (HCP) crystal structures, few direct atomistic studies of twinning have been conducted for other types of low symmetry materials, in large part due to a lack of reliable interatomic potentials. In this work, we examine twin boundary structure and migration in a tetragonal material, β-Sn, comparing high resolution Transmission Electron Microscopy (TEM) images of deformation twins in β-Sn to the results of direct atomistic simulations using multiple interatomic potentials. ML-based potentials developed in this work are found to give results consistent with our experimental data, revealing faceted twin boundary structures formed by the nucleation and motion of twinning disconnections. We use bicrystallographic methods in combination with atomistic simulations to analyze the structure, energy and shear coupled migration of observed twin facets in β-Sn. In analogy to Prismatic-Basal (PB/BP) interfaces in HCP metals, we discover low energy asymmetric Prismatic-A-plane (PA/AP) interfaces important to twin growth in β-Sn. Finally, a Moment Tensor Potential (MTP) and Rapid Artificial Neural Network (RANN) interatomic potential suitable for studying twinning and phase transformations in Sn are made publicly available as part of this work.

36 MATERIALS SCIENCE

Gold–Thiolate Nanocluster Dynamics and Intercluster Reactions Enabled by a Machine Learned Interatomic Potential

Monolayer protected metal clusters comprise a rich class of molecular systems and are promising candidate materials for a variety of applications. While a growing number of protected nanoclusters have been synthesized and characterized in crystalline forms, their dynamical behavior in solution, including prenucleation cluster formation, is not well understood due to limitations both in characterization and first-principles modeling techniques. Recent advancements in machine-learned interatomic potentials are rapidly enabling the study of complex interactions such as dynamical behavior and reactivity on the nanoscale. Here, we develop an Au-S-C-H atomic cluster expansion (ACE) interatomic potential for efficient and accurate molecular dynamics simulations of thiolate-protected gold nanoclusters (Au n (SCH 3 ) m ). Trained on more than 30,000 density functional theory calculations of gold nanoclusters, the interatomic potential exhibits ab initio level accuracy in energies and forces and replicates nanocluster dynamics including thermal vibration and chiral inversion. Long dynamics simulations (up to 0.1 μs time scale) reveal a mechanism explaining the thermal instability of neutral Au 25 (SR) 18 clusters. Specifically, we observe multiple stages of isomerization of the Au 25 (SR) 18 cluster, including a chiral isomer. Additionally, we simulate coalescence of two Au 25 (SR) 18 clusters and observe series of clusters where the formation mechanisms are critically mediated by ligand exchange in the form of [Au-S] n rings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Benchmarking machine learning interatomic potentials via phonon anharmonicity

Abstract 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 ThO 2 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.

interatomic potentials

Parameterizing empirical interatomic potentials for predicting thermophysical properties via an irreducible derivative approach: the case of ThO 2 and UO 2

The accuracy of classical physical property predictions using molecular dynamics simulations is determined by the quality of the interatomic potentials. Here we introduce a training approach for empirical interatomic potentials (EIPs) which is well suited for capturing phonons and phonon-related properties. Our approach is based on direct comparisons of the second- and third-order irreducible derivatives (IDs) between an EIP and the Born–Oppenheimer potential within density functional theory (DFT) calculations. IDs fully exploit space group symmetry and allow for training without redundant information. We demonstrate the fidelity of our approach in the context of ThO 2 and UO 2 , where we optimize parameters of an embedded-atom method potential in addition to core–shell interactions. Our EIPs provide thermophysical properties in good agreement with DFT and outperform widely utilized EIPs for phonon dispersion and thermal conductivity predictions. Reasonable estimates of thermal expansion and formation energies of Frenkel pairs are also obtained.

empirical interatomic potential

Cross-functional transferability in foundation machine learning interatomic potentials

The rapid development of foundation potentials (FPs) in machine learning interatomic potentials demonstrates the possibility for generalizable learning of the universal potential energy surface. The accuracy of FPs can be further improved by bridging the model from lower-fidelity datasets to high-fidelity ones. In this work, we analyze the challenge of this transfer learning (TL) problem within the CHGNet framework. We show that significant energy scale shifts and poor correlations between GGA and r 2 SCAN hinder cross-functional transferability. By benchmarking different TL approaches on the MP-r 2 SCAN dataset, we demonstrate the importance of elemental energy referencing in the TL of FPs. By comparing the scaling law with and without the pre-training on a low-fidelity dataset, we show that significant data efficiency can still be achieved through TL, even with a target dataset of sub-million structures. We highlight the importance of proper TL and multi-fidelity learning in creating next-generation FPs on high-fidelity data.

Huang, Xu [University of California, Berkeley, CA

Modeling phase transformations in Mn-rich disordered rocksalt cathodes with machine-learning interatomic potentials

Mn-rich disordered rocksalt (DRX) cathode materials exhibit a phase transformation from a disordered to a partially disordered spinel-like structure (δ-phase) during electrochemical cycling. Here, in this computational study, we use charge-informed molecular dynamics with a fine-tuned CHGNet foundation potential to investigate the phase transformation in LixMn 0.8 Ti 0.1 O 1.9 F 0.1 . Our results indicate that transition metal migration occurs and reorders to form the spinel-like ordering in an FCC anion framework. The transformed structure contains a higher concentration of nontransition metal (0-TM) face-sharing channels, which are known to improve Li transport kinetics. Analysis of the Mn valence distribution suggests that the appearance of tetrahedral Mn 2+ is a consequence of spinel-like ordering, rather than the trigger for cation migration as previously suggested. Calculated equilibrium intercalation voltage profiles demonstrate that the δ-phase, unlike the ordered spinel, exhibits solid-solution signatures at low voltage. A higher Li capacity is obtained than in the DRX phase. This study provides atomic insights into solid-state phase transformation and its relation to experimental electrochemistry, highlighting the potential of machine-learning interatomic potentials for understanding complex oxide materials.

Zhong, Peichen [University of California, Berkeley

Liquid–Vapor Phase Equilibrium in Molten Aluminum Chloride (AlCl 3 ) Enabled by Machine Learning Interatomic Potentials

Molten salts are promising candidates in numerous clean energy applications, where knowledge of thermophysical properties and vapor pressure across their operating temperature ranges is critical for safe operations. Due to challenges in evaluating these properties using experimental methods, fast and scalable molecular simulations are essential to complement the experimental data. In this study, we developed machine learning interatomic potentials (MLIP) to study the AlCl 3 molten salt across varied thermodynamic conditions (T = 473–613 K and P = 2.7–23.4 bar), which allowed us to predict temperature-surface tension correlations and liquid–vapor phase diagram from direct simulations of two-phase coexistence in this molten salt. Two MLIP architectures, a Kernel-based potential and neural network interatomic potential (NNIP), were considered to benchmark their performance for AlCl 3 molten salt using experimental structure and density values. The NNIP potential employed in two-phase equilibrium simulations yields the critical temperature and critical density of AlCl 3 that are within 10 K (∼3%) and 0.03 g/cm 3 (∼7%) of the reported experimental values. An accurate correlation between temperature and viscosities is obtained as well. In doing so, we report that the inclusion of low-density configurations in their training is critical to more accurately represent the AlCl 3 system across a wide phase-space. The MLIP trained using PBE-D3 functional in the ab initio molecular dynamics (AIMD) simulations (120 atoms) also showed close agreement with experimentally determined molten salt structure comprising Al 2 Cl 6 dimers, as validated using Raman spectra and neutron structure factor. Furthermore, the PBE-D3 as well as its trained MLIP showed better liquid density and temperature correlation for AlCl 3 system when compared to several other density functionals explored in this work. Overall, the demonstrated approach to predict temperature correlations for liquid and vapor densities in this study can be employed to screen nuclear reactors-relevant compositions, helping to mitigate safety concerns.

Ab initio molecular dynamics

Uncertainty quantification for misspecified machine learned interatomic potentials

The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of settings, which has brought renewed interest in robust means to quantify uncertainties. In many practical settings where model complexity is constrained (e.g., due to performance considerations), misspecification — the inability of any one choice of model parameters to exactly match all training data — is a key contributor to errors that is often disregarded. Here, we employ a recent misspecification-aware regression technique to quantify parameter uncertainties, which is then propagated to a broad range of phase and defect properties in tungsten. The propagation is performed through both brute-force resampling and implicit Taylor expansion. The propagated misspecification uncertainties robustly quantify and bound errors on a broad range of material properties. We demonstrate application to recent foundational machine learning interatomic potentials, accurately predicting and bounding errors in MACE-MPA-0 energy predictions across the diverse materials project database.

36 MATERIALS SCIENCE