Energy-based clustering: Fast and robust clustering of data with known likelihood functions.

Clustering has become an indispensable tool in the presence of increasingly large and complex datasets. Most clustering algorithms depend, either explicitly or implicitly, on the sampled density. However, estimated densities are fragile due to the curse of dimensionality and finite sampling effects, for instance, in molecular dynamics simulations. To avoid the dependence on estimated densities, an energy-based clustering (EBC) algorithm based on the Metropolis acceptance criterion is developed in this work. In the proposed formulation, EBC can be considered a generalization of spectral clustering in the limit of large temperatures. Taking the potential energy of a sample explicitly into account alleviates requirements regarding the distribution of the data. In addition, it permits the subsampling of densely sampled regions, which can result in significant speed-ups and sublinear scaling. The algorithm is validated on a range of test systems including molecular dynamics trajectories of alanine dipeptide and the Trp-cage miniprotein. Our results show that including information about the potential-energy surface can largely decouple clustering from the sampled density.

Hybrid classical/machine-learning force fields for the accurate description of molecular condensed-phase systems.

Electronic structure methods offer in principle accurate predictions of molecular properties, however, their applicability is limited by computational costs. Empirical methods are cheaper, but come with inherent approximations and are dependent on the quality and quantity of training data. The rise of machine learning (ML) force fields (FFs) exacerbates limitations related to training data even further, especially for condensed-phase systems for which the generation of large and high-quality training datasets is difficult. Here, we propose a hybrid ML/classical FF model that is parametrized exclusively on high-quality ab initio data of dimers and monomers in vacuum but is transferable to condensed-phase systems. The proposed hybrid model combines our previous ML-parametrized classical model with ML corrections for situations where classical approximations break down, thus combining the robustness and efficiency of classical FFs with the flexibility of ML. Extensive validation on benchmarking datasets and experimental condensed-phase data, including organic liquids and small-molecule crystal structures, showcases how the proposed approach may promote FF development and unlock the full potential of classical FFs.

Regularized by Physics: Graph Neural Network Parametrized Potentials for the Description of Intermolecular Interactions.

Simulations of molecular systems using electronic structure methods are still not feasible for many systems of biological importance. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. The parametrization of FF is, however, time-consuming and has traditionally been based on experimental data. Recent years have therefore seen increasing efforts to automatize FF parametrization or to replace FF with machine-learning (ML) based potentials. Here, we propose an alternative strategy to parametrize FF, which makes use of ML and gradient-descent based optimization while retaining a functional form founded in physics. Using a predefined functional form is shown to enable interpretability, robustness, and efficient simulations of large systems over long time scales. To demonstrate the strength of the proposed method, a fixed-charge and a polarizable model are trained on ab initio potential-energy surfaces. Given only information about the constituting elements, the molecular topology, and reference potential energies, the models successfully learn to assign atom types and corresponding FF parameters from scratch. The resulting models and parameters are validated on a wide range of experimentally and computationally derived properties of systems including dimers, pure liquids, and molecular crystals.

Learning Atomic Multipoles: Prediction of the Electrostatic Potential with Equivariant Graph Neural Networks.

The accurate description of electrostatic interactions remains a challenging problem for classical potential-energy functions. The commonly used fixed partial-charge approximation fails to reproduce the electrostatic potential at short range due to its insensitivity to conformational changes and anisotropic effects. At the same time, possibly more accurate machine-learned (ML) potentials struggle with the long-range behavior due to their inherent locality ansatz. Employing a multipole expansion offers in principle an exact treatment of the electrostatic potential such that the long-range and short-range electrostatic interactions can be treated simultaneously with high accuracy. However, such an expansion requires the calculation of the electron density using computationally expensive quantum-mechanical (QM) methods. Here, we introduce an equivariant graph neural network (GNN) to address this issue. The proposed model predicts atomic multipoles up to the quadrupole, circumventing the need for expensive QM computations. By using an equivariant architecture, the model enforces the correct symmetry by design without relying on local reference frames. The GNN reproduces the electrostatic potential of various systems with high fidelity. Possible uses for such an approach include the separate treatment of long-range interactions in ML potentials, the analysis of electrostatic potential surfaces, and static multipoles in polarizable force fields.

Machine Learning in QM/MM Molecular Dynamics Simulations of Condensed-Phase Systems.

Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations have been developed to simulate molecular systems, where an explicit description of changes in the electronic structure is necessary. However, QM/MM MD simulations are computationally expensive compared to fully classical simulations as all valence electrons are treated explicitly and a self-consistent field (SCF) procedure is required. Recently, approaches have been proposed to replace the QM description with machine-learned (ML) models. However, condensed-phase systems pose a challenge for these approaches due to long-range interactions. Here, we establish a workflow, which incorporates the MM environment as an element type in a high-dimensional neural network potential (HDNNP). The fitted HDNNP describes the potential-energy surface of the QM particles with an electrostatic embedding scheme. Thus, the MM particles feel a force from the polarized QM particles. To achieve chemical accuracy, we find that even simple systems require models with a strong gradient regularization, a large number of data points, and a substantial number of parameters. To address this issue, we extend our approach to a Δ-learning scheme, where the ML model learns the difference between a reference method (density functional theory (DFT)) and a cheaper semiempirical method (density functional tight binding (DFTB)). We show that such a scheme reaches the accuracy of the DFT reference method while requiring significantly less parameters. Furthermore, the Δ-learning scheme is capable of correctly incorporating long-range interactions within a cutoff of 1.4 nm. It is validated by performing MD simulations of retinoic acid in water and the interaction between S-adenoslymethioniat and cytosine in water. The presented results indicate that Δ-learning is a promising approach for (QM)ML/MM MD simulations of condensed-phase systems.