Gaussian Process-Based Refinement of Dispersion Corrections

Abstract

We employ Gaussian process (GP) regression to adjust for systematic errors in D3-type dispersion corrections introducing the associated, statistically improved model D3-GP. We generated a data set containing interaction energies for 1,248 molecular dimers, which resemble the dispersion-dominated systems contained in the S66 data set. Our systems do not only represent equilibrium structures, but also dimers with various relative orientations and conformations at both shorter and longer distances. To train our D3-GP model, we engineered two different vectorial representations of (supra-)molecular systems, both derived from the matrix of atom-pairwise D3(BJ) interaction terms: (a) a distance-resolved interaction energy histogram and (b) eigenvalues of the interaction matrix ordered according to their decreasing absolute value. We harness the prediction variance obtained from GP regression to select optimal training sets in an automated fashion. The larger the variance, the more information the corresponding data point may add to the training set. For a given set of molecular systems, variance-based sampling can approximately determine the smallest subset being subjected to reference calculations such that all dispersion corrections for the remaining systems fall below a predefined accuracy threshold. Our refined learning algorithm selects multiple (instead of single) systems which can be subjected to reference calculations simultaneously. We refer to the underlying selection strategy as batch-wise variance-based sampling (BVS). BVS-guided active learning is an essential component of our D3-GP workflow, which is implemented in a black-box fashion. This approach leads overall to a self-improving model (D3-GP) that predicts system-focused and GP-refined D3-type dispersion corrections for any given system of reference data.

arXiv comment25 pages, 5 figures

References in corpus (19)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• On representing chemical environments
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Nonlocal van der Waals density functional: The simpler the better
• Big Data meets Quantum Chemistry Approximations: The $\Delta$-Machine Learning Approach
• Less is more: sampling chemical space with active learning
• By-passing the Kohn-Sham equations with machine learning
• Alchemical and structural distribution based representation for improved QML
• A Transferable Machine-Learning Model of the Electron Density
• Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning
• Machine learning of molecular properties: locality and active learning
• Error-Controlled Exploration of Chemical Reaction Networks with Gaussian Processes
• Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes
• Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space
• Equation of state of fluid methane from first principles with machine learning potentials
• Reliable estimation of prediction uncertainty for physico-chemical property models
• Error Assessment of Computational Models in Chemistry
• Statistical Analysis of Semiclassical Dispersion Corrections
• Efficient prediction of 3D electron densities using machine learning

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