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We consider the quantum creation of a closed universe within the Euclidean path-integral formalism. An analytical expression for the tunneling probability is derived, including both the exponential suppression and the exact Gaussian…
An artificial neural network (ANN) is investigated as a tool for estimating rate coefficients for the collisional excitation of molecules. The performance of such a tool can be evaluated by testing it on a dataset of collisionally-induced…
A consistent theory of the ground state energy and its splitting due to the process of tunneling for the Lipkin model is presented. For the functional integral in terms of the spin coherent states for the partition function of the model we…
Reaction rates are a complicated function of molecular interactions, which can be selected from vast chemical design spaces. Seeking the design that optimizes a rate is a particularly challenging problem since the rate calculation for any…
Beyond the conventional trial-and-error method, machine learning offers a great opportunity to accelerate the discovery of functional materials, but still often suffers from difficulties such as limited materials data and unbalanced…
We present a new efficient transition pathway search method based on the least action principle and the Gaussian process regression method. Most pathway search methods developed so far rely on string representations, which approximate a…
Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy…
A dataset of fully quantum flux-flux correlation functions and reaction rate constants was constructed for organic heterogeneous catalytic surface reactions. Gaussian process regressors were successfully fitted to training data to predict…
We introduce a machine-learning interatomic potential for tungsten using the Gaussian Approximation Potential framework. We specifically focus on properties relevant for simulations of radiation-induced collision cascades and the damage…
A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [$\textit{ J.…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
Artificial neural networks (NNs) are one of the most frequently used machine learning approaches to construct interatomic potentials and enable efficient large-scale atomistic simulations with almost ab initio accuracy. However, the…
The development of computational models for the numerical simulation of chemically reacting flows operating in the turbulent regime requires the solution of partial differential equations that represent the balance of mass, linear momentum,…
We propose a fast and accurate numerical method for pricing European swaptions in multi-factor Gaussian term structure models. Our method can be used to accelerate the calibration of such models to the volatility surface. The pricing of an…
A massively parallel method to build large transition rate matrices from temperature accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state…
Motivated by a large ground-level ozone dataset, we propose a new computationally efficient additive approximate Gaussian process. The proposed method incorporates a computational-complexity-reduction method and a separable covariance…
Individualized treatment rule (ITR) recommends treatment on the basis of individual patient characteristics and the previous history of applied treatments and their outcomes. Despite the fact there are many ways to estimate ITR with binary…
We propose a novel group of Gaussian Process based algorithms for fast approximate optimal stopping of time series with specific applications to financial markets. We show that structural properties commonly exhibited by financial time…