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The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
We use semiclassical methods to calculate the probability of inducing a change of topology via a high-energy collision in the SU(2)-Higgs theory. This probability is determined by a complex solution to a classical boundary value problem on…
For machine learning of interatomic potentials a scalable sparse Gaussian process regression formalism is introduced with a data-efficient on-the-fly adaptive sampling algorithm. With this approach, the computational cost is effectively…
Machine learned force fields typically require manual construction of training sets consisting of thousands of first principles calculations, which can result in low training efficiency and unpredictable errors when applied to structures…
We generalize the string method, originally designed for the study of thermally activated rare events, to the calculation of quantum tunneling rates. This generalization is based on the analogy between quantum mechanics and statistical…
Microcanonical instanton theory offers the promise of providing rate constants for chemical reactions including quantum tunneling of atoms over the whole temperature range. We discuss different rate expressions, which require the…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present…
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics…
We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. We derive a generalization of instanton theory for these asymmetric…
The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In…
A method to derive the corrections for the dispersion of the reaction plane at intermediate energies is proposed. The method is based on the correlated, non-isotropic Gaussian approximation. It allowed to construct the excitation function…
The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However,…
A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the…
Path integral implementation of the quantum instanton approximation currently belongs among the most accurate methods for computing quantum rate constants and kinetic isotope effects, but its use has been limited due to the rather high…
Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the…