Fast proper orthogonal descriptors for many-body interatomic potentials

Machine learning (ML) interatomic potentials (ML-IAPs) are generated for alkane and polyene hydrocarbons using on-the-fly adaptive sampling and a sparse Gaussian process regression (SGPR) algorithm. The ML model is generated based on the PBE+D3 level of density functional theory (DFT) with molecular dynamics (MD) for small alkane and polyene molecules. Intermolecular interactions are also trained with clusters and condensed phases of small molecules. It shows excellent transferability to long alkanes and closely describes the ab inito potential energy surface for polyenes. Simulation of liquid ethane also shows reasonable agreement with experimental reports. This is a promising initiative toward a universal ab initio quality force-field for hydrocarbons and organic molecules.

We introduce a new class of machine learning interatomic potentials---fast general two- and three-body potential (GTTP), which is as fast as conventional empirical potentials and require computational time that remains constant with increasing fitting flexibility. GTTP does not contain any assumptions about the functional form of two- and three-body interactions. These interactions can be modeled arbitrarily accurately, potentially by thousands of parameters not affecting resulting computational cost. Time complexity is O(1) per every considered pair or triple of atoms. The fitting procedure is reduced to simple linear regression on ab initio calculated energies and forces and leads to effective two- and three-body potential, reproducing quantum many-body interactions as accurately as possible. Our potential can be made continuously differentiable any number of times at the expense of increased computational time. We made a number of performance tests on one-, two- and three-component systems. The flexibility of the introduced approach makes the potential transferable in terms of size and type of atomic systems as long as they involve the same atomic species. We show that trained on randomly generated structures with just eight atoms in the unit cell, it significantly outperforms common empirical interatomic potentials in the study of large systems, such as grain boundaries in polycrystalline materials.

Dopants can tune the performance of MoS2 in various applications, but the use of molecular dynamics simulations for doped MoS2 materials discovery is limited by the lack of multidopant interatomic potentials. Universal machine learning interatomic potentials (MLIPs) could be a solution, but the accuracy of these potentials must first be evaluated. Here, we evaluate the accuracy of a recently developed MLIP, META's Universal Model for Atoms, for 25 different MoS2 dopants spanning metals, nonmetals, and transition metals in Mo-substitution, S-substitution, and intercalated positions by benchmarking the MLIP-predicted formation energy and the dopant-induced structural change against density functional theory (DFT) calculations. The computational framework for MLIP validation and simulations is described in detail, and the source code is made available online. The MLIP is then demonstrated by performing heating-cooling simulations of MoS2 supercells with all 25 dopants. These simulations capture complex phenomena including dopant clustering, MoS2 layer fracturing, interlayer diffusion, and chemical compound formation at orders-of-magnitude reduced computational cost compared to DFT. This work provides a computational workflow for the application-oriented design of doped-MoS2, enabling high-throughput screening of dopant candidates and optimization of compositions for targeted tribological, electronic, and optoelectronic performance.

A comparison of molecular dynamics potentials used to account for thermal diffuse scattering in multislice simulations

Recent developments in machine learning interatomic potentials (MLIPs) have empowered even nonexperts in machine learning to train MLIPs for accelerating materials simulations. However, reproducibility and independent evaluation of presented MLIP results is hindered by a lack of clear standards in current literature. In this Perspective, we aim to provide guidance on best practices for documenting MLIP use while walking the reader through the development and deployment of MLIPs including hardware and software requirements, generating training data, training models, validating predictions, and MLIP inference. We also suggest useful plotting practices and analyses to validate and boost confidence in the deployed models. Finally, we provide a step-by-step checklist for practitioners to use directly before publication to standardize the information to be reported. Altogether, we hope that our work will encourage the reliable and reproducible use of these MLIPs, which will accelerate their ability to make a positive impact in various disciplines including materials science, chemistry, and biology, among others.

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning, which uses biased or unbiased molecular dynamics (MD) to generate candidate pools, aims to address this objective. Existing biased and unbiased MD-simulation methods, however, are prone to miss either rare events or extrapolative regions—areas of the configurational space where unreliable predictions are made. This work demonstrates that MD, when biased by the MLIP’s energy uncertainty, simultaneously captures extrapolative regions and rare events, which is crucial for developing uniformly accurate MLIPs. Furthermore, exploiting automatic differentiation, we enhance bias-forces-driven MD with the concept of bias stress. We employ calibrated gradient-based uncertainties to yield MLIPs with similar or, sometimes, better accuracy than ensemble-based methods at a lower computational cost. Finally, we apply uncertainty-biased MD to alanine dipeptide and MIL-53(Al), generating MLIPs that represent both configurational spaces more accurately than models trained with conventional MD.

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

Machine learning interatomic potentials (MLIPs) enable more efficient molecular dynamics (MD) simulations with ab initio accuracy, which have been used in various domains of physical science. However, distribution shift between training and test data causes deterioration of the test performance of MLIPs, and even leads to collapse of MD simulations. In this work, we propose an online Test-time Adaptation Interatomic Potential (TAIP) framework to improve the generalization on test data. Specifically, we design a dual-level self-supervised learning approach that leverages global structure and atomic local environment information to align the model with the test data. Extensive experiments demonstrate TAIP’s capability to bridge the domain gap between training and test dataset without additional data. TAIP enhances the test performance on various benchmarks, from small molecule datasets to complex periodic molecular systems with various types of elements. TAIP also enables stable MD simulations where the corresponding baseline models collapse.

We introduced a novel machine-learned interatomic potential (MLIP) by thoroughly discussing the step–by–step MLIP creation process using precise but limited data. This study explored the mechanical properties of hexagonal boron nitride (hBN) nanosheets and addressed the challenges of accurately predicting their structural properties. We explored the use of ab initio molecular dynamics and classical molecular dynamics (CMD) simulation techniques, emphasizing the necessity for a more effective and efficient solution. We also discussed the machine learning procedure to construct an effective interatomic potential. Furthermore, we address techniques for evaluating the performance and robustness of MLIPs on unseen datasets. Using the newly formed MLIP in a CMD simulation, we investigated the mechanical attributes of hBN nanosheets, exploring the fluctuations in sheet strength across a range of dimensions, temperatures, and varying numbers of layers. We obtained an average Young’s modulus in the range of 980–1000 GPa at 1 K, whereas the average failure stress and strain were approximately 106 GPa and 0.16, respectively. Our results demonstrate significant improvements in the accuracy of hBN nanosheets compared to prior studies, highlighting the effectiveness of MLIP in achieving higher precision with minimal computational cost. This study offers comprehensive analysis and theoretical exploration, delivering valuable insights into MLIP and the mechanical properties of hBN nanosheets, and paves the way for future applications in materials science and engineering.

The suppression of heat transport in disordered crystals arises from a competition between mass fluctuations and bond disorder, but their relative contributions remain difficult to disentangle. We address this challenge using a machine-learned interatomic potential trained on ab initio data across the PbTe1-xSex alloy series. Molecular dynamics simulations with the trained machine-learned interatomic potential reproduce experimental lattice thermal conductivities and density-functional theory phonon dispersions while enabling frequency-resolved analysis of heat transport from 300 to 800 K. We find a narrow window near 1.7-2.0 THz dominates heat transport across all compositions, where heat is primarily carried by mixed longitudinal acoustic and optical modes. Alloying dramatically reduces spectral diffusivity near 2 THz leading to the deterioration of thermal conductivity. For the parent compounds both the spectral diffusivity and overall thermal conductivity decrease at elevated temperatures. However, the thermal degradation is weaker for the mid-range composition (x = 0.5) due to the greater thermal occupation of vibrational modes and increased heat capacity. Alchemical simulations show that force-constant disorder, not mass contrast, plays the dominant role in this suppression. These results highlight the microscopic mechanisms underlying thermal transport breakdown in alloys and demonstrate how machine-learned interatomic potentials now offer a tractable path toward predictive, physics-rich thermal transport modeling in complex disordered solids.

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 ThO2and UO2, 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.

The integration ofmachine learning into reactive chemistry, materialsdiscovery, and drug design is transforming the development of novelmolecules and materials. Machine Learning Interatomic Potentials (MLIPs)predict potential energies and forces with quantum chemistry accuracy,surpassing traditional approaches. Incorporating force fitting inMLIP training enhances potential-energy surface predictions and improvesmodel transferability and reliability. This paper introduces and evaluatesthe integration of Hessian matrix training in MLIPs, which encodessecond-order information about the PES curvature. Our evaluation focuseson models trained only to equilibrium geometries and first-order saddlepoints (i.e., critical points on the potential surface), demonstratingtheir ability to extrapolate to nonequilibrium geometries. This integrationimproves extrapolation capabilities, allowing MLIPs to accuratelypredict energies, forces, and Hessian predictions for nonequilibriumgeometries. Hessian-trained MLIPs enhance reaction pathway modeling,transition state identification, and vibrational spectra predictions,benefiting molecular dynamics (MD) simulations and Nudged ElasticBand (NEB) calculations. By analyzing models trained with varyingcombinations of energy, force, and Hessian data on a small moleculereactive data set, we demonstrate that models including Hessian informationnot only extrapolate more accurately to unseen molecular systems,improving accuracy in reaction modeling and vibrational analysis,but also reduce the total amount of data required for effective training.However, the primary trade-off is increased computational expense,as Hessian training requires more resources than conventional energy-forcetraining. Our findings provide comprehensive insights into the advantagesand limitations of Hessian integration in MLIP training, allowingpractitioners in computational chemistry to make informed decisionsabout employing this method in accordance with their specific researchobjectives and computational constraints.

<title>Abstract</title> Machine-Learning Interatomic Potentials (MLIPs) have surged in popularity due to their promise of expanding the spatiotemporal scales possible for simulating molecules with high fidelity. The accuracy of any MLIP is dependent on the data used for its training; thus, for large molecules, like polymers, where accurate training data is prohibitively difficult to obtain, it becomes necessary to pursue non-traditional methods to construct MLIPs, many of which are based on constructing MLIPs using smaller, analogous chemical systems. However, we have yet to understand the limits to which smaller molecules can be used as a proxy for extrapolating macromolecular energetics. Here, we provide a ''control study'' for such experiments, exploring the ability of MLIP approaches to extrapolate between n=1-8 n-polyalkanes at identical conditions. Through Principal Covariates Classification, we quantitatively demonstrate how convergence in chemical environments between training and testing datasets coincides with an MLIP's transferability. Additionally, we show how careful attention to the construction of an MLIP's neighbor list can promote greater transferability when considering various levels of the energetic hierarchy. Our results establish a roadmap for how one can create transferable MLIPs for macromolecular systems without the prohibitive cost of constructing system-specific training data.

Chemical heuristics have been fundamental to the advancement of chemistry and materials science. These heuristics are typically established by scientists using knowledge and creativity to extract patterns from limited datasets. Machine learning offers opportunities to perfect this approach using computers and larger datasets. Here, we discuss the relationships between traditional heuristics and machine learning approaches. We show how traditional rules can be challenged by large-scale statistical assessment and how traditional concepts commonly used as features are feeding the machine learning techniques. We stress the waste involved in relearning chemical rules and the challenges in terms of data size requirements for purely data-driven approaches. Our view is that heuristic and machine learning approaches are at their best when they work together.

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids-including the density response, surface tension and size-dependent cavitation free energies-for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.