Machine-learned potentials for solvation modeling

Machine learning potentials (MLPs) can enable simulations of ab initio accuracy at orders of magnitude lower computational cost. However, their effectiveness hinges on the availability of considerable data sets to ensure robust generalization across chemical space and thermodynamic conditions. The generation of such data sets can be labor-intensive, highlighting the need for innovative methods to train MLPs in data-scarce scenarios. Here, we introduce transfer learning of potential energy surfaces between chemically similar elements. Specifically, we leverage the trained MLP for silicon to initialize and expedite the training of an MLP for germanium. Utilizing classical force field and ab initio data sets, we demonstrate that transfer learning surpasses traditional training from scratch in force prediction, leading to more stable simulations and improved temperature transferability. These advantages become even more pronounced as the training data set size decreases. We also observe positive transfer learning effects for most out-of-target properties. Our findings demonstrate that transfer learning across chemical elements is a promising technique for developing accurate and numerically stable MLPs, particularly in a data-scarce regime.

Accurate prediction of the mechanical and thermal properties of CO₂ hydrates is essential for their applications in carbon sequestration and refrigeration, yet remains challenging with empirical forcefields. In this work, a deep potential machine learning potential for CO₂ hydrate, trained on density functional theory datasets, is for the first time developed to serve as a unified and accurate computational framework. The as-developed deep potential machine learning potential achieves near-density functional theory accuracy in energy, force, and virial stress predictions while enabling large-scale molecular dynamics simulations at significantly reduced computational cost. Uniaxial stress-strain analyses demonstrate that the model captures the tensile strength and progressive ductile-like failure behavior. Thermal conductivity prediction agrees closely with experimental measurements within 2% deviation, outperforming empirical forcefields. Vibrational dynamics and phonon analyses reveal that the deep potential machine learning potential more accurately describes the anharmonicity and phonon scattering, especially in high-frequency modes, yielding physically realistic thermal transport behavior. This work establishes deep potential machine learning potential as a robust tool for advancing CO₂ hydrate-based technologies by providing a path for accurate and efficient multi-property prediction. Document Type: Original article Cited as: Xiong, K., Li, Y., Lin, Z., Luo, G., Wu, J. Machine learning potential insights into mechanical response and heat transfer in CO₂ hydrate. Advances in Geo-Energy Research, 2025, 18(1): 38-50. https://doi.org/10.46690/ager.2025.10.04

Recent theoretical studies of the van der Waals complexes formed between water and the two main components of air, nitrogen and oxygen, are reviewed. Combined with previous work on the water–argon complex, the results allow non-ideal thermodynamic properties of water–air mixtures to be calculated. The intermolecular potential energy surfaces for these complexes have been calculated using a combination of supermolecule methods and perturbation theory, as described in a previous review. Theoretical techniques introduced since this previous work include the extension of the intermolecular perturbation theory to open-shell electronic species, as required for the water–oxygen complex, and new and more accurate calculations of dispersion energy coefficients. Spin-unrestricted, time-dependent coupled cluster theory has been used for calculating dispersion energy coefficients for the water–oxygen complex, and this method is described and compared with other accurate methods, and a possible alternative method is suggested for future work. The results obtained for the water–nitrogen complex are highly satisfactory. With little more computational effort than is required to produce a second-order Moller–Plesset supermolecule potential energy surface, the intermolecular potential is calculated to an accuracy which appears to be comparable to coupled-cluster calculations with perturbative triple excitations. For the water–oxygen complex, the different theoretical methods produce potential energy surfaces with larger discrepancies than for water–nitrogen, although they predict the main features of the potential energy surface better than calculations in the literature. Although few experimental measurements of water–oxygen virial coefficients are available, the agreement of theoretical predictions with these is reasonable, and the agreement with the better characterized water–air virial coefficients is very good. The review concludes with a forward look to work on larger molecules. Increasing the size of the interacting molecules creates a number of practical problems. Some problems, including the steep scaling of computation time with system size, are common to all methods. The use in the current work of a damped multipole expansion about the molecular centres also causes problems when larger molecules are considered. The review therefore considers methods that can be used to reduce the unfavourable size scaling, to reduce the size of the basis set, and to use damped atomic multipole expansions, which are centred on the nuclei of the interacting molecules.

Global optimization of atomistic structure relies on the generation of new candidate structures in order to drive the exploration of the potential energy surface (PES) in search of the global minimum energy structure. In this work, we discuss a type of structure generation, which locally optimizes structures in complementary energy (CE) landscapes. These landscapes are formulated temporarily during the searches as machine learned potentials (MLPs) using local atomistic environments sampled from collected data. The CE landscapes are deliberately incomplete MLPs that rather than mimicking every aspect of the true PES are sought to become much smoother, having only a few local minima. This means that local optimization in the CE landscapes may facilitate the identification of new funnels in the true PES. We discuss how to construct the CE landscapes and we test their influence on the global optimization of a reduced rutile SnO2(110)-(4 × 1) surface and an olivine (Mg2SiO4)4 cluster for which we report a new global minimum energy structure.

The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chemical space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach, we develop the COmprehensive Machine-learning Potential (COMP6) benchmark (publicly available on GitHub) which contains a diverse set of organic molecules. Active learning-based ANI potentials outperform the original random sampled ANI-1 potential with only 10% of the data, while the final active learning-based model vastly outperforms ANI-1 on the COMP6 benchmark after training to only 25% of the data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single molecules or materials, while remaining applicable to the general class of organic molecules composed of the elements CHNO.

Inexpensive machine learning (ML) potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al. J. Chem. Phys., 2018, 148, 241733.) and Transition1x (Schreiner et al. Sci. Data, 2022, 9, 779.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials.

Machine learning potential has become increasingly successful in atomistic simulations. Many of these potentials are based on an atomistic representation in a local environment, but an efficient description of nonlocal interactions that exceed a common local environment remains a challenge. Herein, we propose a simple and efficient equivariant model, EquiREANN, to effectively represent a nonlocal potential energy surface. It relies on a physically inspired message-passing framework, where the fundamental descriptors are linear combinations of atomic orbitals, while both invariant orbital coefficients and the equivariant orbital functions are iteratively updated. We demonstrate that this EquiREANN model is able to describe the subtle potential energy variation due to the nonlocal structural change with high accuracy and little extra computational cost than an invariant message passing model. Our work offers a generalized approach to create equivariant message-passing adaptations of other advanced local many-body descriptors.

The Front Cover evokes particle swarm optimization applied to Bi–Pt bimetallic nanoparticles. Each bird represents a candidate nanoparticle structure. The lake and its shorelines represent the potential energy surface, generated using the ChiMES physics-informed machine learning potential. The surrounding mountains symbolize transition states, while the dark whirlpool at the lake’s center is the global energy minimum. More information can be found in the Research Article by N. T. Van-Oanh and co-workers (DOI: 10.1002/cphc.202500268).

Due to the increased concern about energy and environmental issues, significant attention has been paid to the development of large-scale energy storage devices to facilitate the utilization of clean energy sources. The redox flow battery (RFB) is one of the most promising systems. Recently, the high cost of transition-metal complex-based RFB has promoted the development of aqueous RFBs with redox-active organic molecules. To expand the working voltage, computational chemistry has been applied to search for organic molecules with lower or higher redox potentials. However, redox potential computation based on implicit solvation models would be challenging due to difficulty in parametrization when considering the complex solvation of supporting electrolytes. Besides, although ab initio molecular dynamics (AIMD) describes the supporting electrolytes with the same level of electronic structure theory as the redox couple, the application is impeded by the high computation costs. Recently, machine learning molecular dynamics (MLMD) has been illustrated to accelerate AIMD by several orders of magnitude without sacrificing the accuracy. It has been established that redox potentials can be computed by MLMD with two separated machine learning potentials (MLPs) for reactant and product states, which is redundant and inefficient. In this work, an automated workflow is developed to construct a universal MLP for both states, which can compute the redox potentials or acidity constants of redox-active organic molecules more efficiently. Furthermore, the predicted redox potentials can be evaluated at the hybrid functional level with much lower costs, which would facilitate the design of aqueous organic RFBs.

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

The use of parallel tempering or replica exchange molecular dynamics (REMD) simulations has facilitated the exploration of free energy landscapes for complex molecular systems, but application to large systems is hampered by the scaling of the number of required replicas with increasing system size. Use of continuum solvent models reduces system size and replica requirements, but these have been shown to provide poor results in many cases, including overstabilization of ion pairs and secondary structure bias. Hybrid explicit/continuum solvent models can overcome some of these problems through an explicit representation of water molecules in the first solvation shells, but these methods typically require restraints on the solvent molecules and show artifacts in water properties due to the solvation interface. We propose an REMD variant in which the simulations are performed with a fully explicit solvent, but the calculation of exchange probability is carried out using a hybrid model, with the solvation shells calculated on the fly during the fully solvated simulation. The resulting reduction in the perceived system size in the REMD exchange calculation provides a dramatic decrease in the computational cost of REMD, while maintaining a very good agreement with results obtained from the standard explicit solvent REMD. We applied several standard and hybrid REMD methods with different solvent models to alanine polymers of 1, 3, and 10 residues, obtaining ensembles that were essentially independent of the initial conformation, even with explicit solvation. Use of only a continuum model without a shell of explicit water provided poor results for Ala3 and Ala10, with a significant bias in favor of the α-helix. Likewise, using only the solvation shells and no continuum model resulted in ensembles that differed significantly from the standard explicit solvent data. Ensembles obtained from hybrid REMD are in very close agreement with explicit solvent data, predominantly populating polyproline II conformations. Inclusion of a second shell of explicit solvent was found to be unnecessary for these peptides.

Several experimental studies suggest that GPCR dimers or oligomers may play an important role in signal transduction. In 2011 the crystal structure of a hβ2R-Gαβγ-complex was published and crystal structures of GPCR dimers are known. But until now, no crystal structure of a GPCR dimer including the Gαβγ-complex is available. In order to obtain detailed insights into interactions within hβ2R dimers including the Gαβγ-complex we performed a potential-energy-surface scan in order to identify favored asymmetric and symmetric hβ2R-Gαβγ-homodimers. This potential energy surface scan suggests, besides the existence of asymmetric dimers, the existence of a symmetric hβ2R-Gαβγ-homodimer with a TM I/VII-contact. A subsequent 20 ns MD simulation of the symmetric homodimer revealed large asymmetric conformational changes of both hβ2Rs, especially regarding TM VII and the interaction network between Asp(2.50), Val(7.44), Ser(7.46) and Tyr(7.43). Since similar conformational changes were not observed during the molecular dynamic simulation of the monomeric hβ2R-Gαβγ-complex, it may be suggested that the conformational changes in the symmetric homodimer are related to the presence of the second hβ2R-Gαβγ-complex. Due to the limitations of simulation time, conformational changes within a time scale of μs or ms may of course not be observed. However, the detected conformational changes, especially in TM VII, correspond to minima on the potential energy surface and thus, this study gives new insights into GPCR dimers on molecular level and furthermore, gives suggestions for site-directed mutagenesis studies.

Investigating reconstructive phase transitions in large-sized systems requires a highly efficient computational framework with computational cost proportional to the system size. Traditionally, widely used frameworks such as density functional theory (DFT) have been prohibitively expensive for extensive simulations on large systems that require long-time scales. To address this challenge, this study employed well-trained machine learning potential to simulate phase transitions in a large-size system. This work integrates the metadynamics simulation approach with machine learning potential, specifically deep potential, to enhance computational efficiency and accelerate the study of phase transition and consequent development of grains and dislocation defects in a system. The new method is demonstrated using the phase transitions of bulk silicon under high pressure. This approach has revealed the transition path and formation of polycrystalline silicon systems under specific stress conditions, demonstrating the effectiveness of deep potential-driven metadynamics simulations in gaining insights into complex material behaviors in large-sized systems.

It is imperative to have highly conductive oxide ion and proton conductors that operate at intermediate temperatures to improve the performance of ceramic fuel cells. The crystal structures of these materials significantly influence their ionic conduction properties. Identifying novel materials with enhanced conductive abilities is a crucial research focus, promising substantial advancements in future fuel cell technologies.In pursuing this goal, we focus on advanced perovskite solid electrolytes and their interfaces. Employing atomistic simulations, we aim to unravel the complexities of these materials, gaining a detailed understanding of ion transport mechanisms crucial for optimising electrolyte performance and efficiency. Our approach integrates the predictive capabilities of density functional theory with the dynamic nature of molecular dynamics, supplemented by machine-learning-based potentials for a thorough analysis.To address larger system sizes and extended time scales in our modelling, we utilise machine learning potentials, specifically moment tensor potentials (MTPs) [1]. The crucial potential fitting process relies on energies, forces, and stresses obtained from diverse configurations through ab initio calculations [2]. Our study focuses on the systems Sr3V2O8 and Ba7Nb4MoO20, and our employed MTPs, fitted using active learning, exhibit excellent agreement with data from ab initio molecular dynamics (AIMD). Notably, oxygen and protons' diffusion coefficients, along with the conductivity of oxygen ions and protons, show commendable consistency with both AIMD simulations and experimental data. This alignment underscores the accuracy and reliability of our MTPs in capturing the intricate dynamics of these materials, reinforcing their suitability for modelling and predicting the behaviour of Sr3V2O8 and Ba7Nb4MoO20. Reference Shapeev, A.V., 2016. Multiscale Modeling & Simulation, 14(3), pp.1153-1173. B. Grabowski, Y. Ikeda, P. Srinivasan, F. Körmann,C. Freysoldt, A. I. Duff, A. Shapeev, J. Neugebauer,npj Computational Materials5 (1) (2019) 1–6.

Protein dynamics is a manifestation of the complex trajectories of these biomolecules on a multidimensional rugged potential energy surface (PES) driven by thermal energy. At present, computational methods such as atomistic molecular dynamics (MD) simulations can describe thermal protein conformational changes in fully solvated environments over millisecond timescales. Despite these advances, a quantitative assessment of protein dynamics remains a complicated topic, intricately linked to issues such as sampling convergence and the identification of appropriate reaction coordinates/structural features to describe protein conformational states and motions. Here, we present the cumulative variance of atomic coordinate fluctuations (CVCF) along trajectories as an intuitive PES sensitive metric to assess both the extent of sampling and protein dynamics captured in MD simulations. We first examine the sampling problem in model one- (1D) and two-dimensional (2D) PES to demonstrate that the CVCF when traced as a function of the sampling variable (time in MD simulations) can identify local and global equilibria. Further, even far from global equilibrium, a situation representative of standard MD trajectories of proteins, the CVCF can distinguish different PES and therefore resolve the resultant protein dynamics. We demonstrate the utility of our CVCF analysis by applying it to distinguish the dynamics of structurally homologous proteins from the ubiquitin family (ubiquitin, SUMO1, SUMO2) and ubiquitin protein-protein interactions. Our CVCF analysis reveals that differential side-chain dynamics from the structured part of the protein (the conserved β-grasp fold) present distinct protein PES to distinguish ubiquitin from SUMO isoforms. Upon binding to two functionally distinct protein partners (UBCH5A and UEV), intrinsic ubiquitin dynamics changes to reflect the binding context even though the two proteins have similar binding modes, which lead to negligible (sub-angstrom scale) structural changes.