8 papers
Fast Multitask Gaussian Process Regression
Aleksei G. Sorokin, Pieterjan Robbe, Fred J. Hickernell
Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (ta…
Credible Intervals for Probability of Failure with Gaussian Processes
Aleksei G. Sorokin, Vishwas Rao
Estimating the probability of failure for expensive simulations is a central task in reliability analysis for structural design, power grid design, and safety certification, among…
Empirical Bernstein and betting confidence intervals for randomized quasi-Monte Carlo
Aadit Jain, Fred J. Hickernell, Art B. Owen +1
Randomized quasi-Monte Carlo (RQMC) methods estimate the mean of a random variable by sampling an integrand at equidistributed points. For scrambled digital nets, the resulting…
Algorithms and Scientific Software for Quasi-Monte Carlo, Fast Gaussian Process Regression, and Scientific Machine Learning
Aleksei G. Sorokin
Most scientific domains elicit the development of efficient algorithms and accessible scientific software. This thesis unifies our developments in three broad domains: Quasi-Monte…
Operator Learning at Machine Precision
Aras Bacho, Aleksei G. Sorokin, Xianjin Yang +6
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing th…
Fast Bayesian Multilevel Quasi-Monte Carlo
Aleksei G. Sorokin, Pieterjan Robbe, Gianluca Geraci +2
Existing multilevel quasi-Monte Carlo (MLQMC) methods often rely on multiple independent randomizations of a low-discrepancy (LD) sequence to estimate statistical errors on each le…