Related papers: Robust designs for Gaussian process emulation of c…
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…
The simulation of the two-dimensional Ising model is used as a benchmark to show the computational capabilities of Graphic Processing Units (GPUs). The rich programming environment now available on GPUs and flexible hardware capabilities…
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
Reinforcement learning provides a framework for learning to control which actions to take towards completing a task through trial-and-error. In many applications observing interactions is costly, necessitating sample-efficient learning. In…
Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of…
High-fidelity simulations and physical experiments are essential for engineering analysis and design, yet their high cost often makes two critical tasks--global sensitivity analysis (GSA) and optimization--prohibitively expensive. This…
Not being able to understand and predict the behavior of deep learning systems makes it hard to decide what architecture and algorithm to use for a given problem. In science and engineering, modeling is a methodology used to understand…
Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine…
Diverse domains of science and engineering use parameterised mechanistic models. Engineers and scientists can often hypothesise several rival models to explain a specific process or phenomenon. Consider a model discrimination setting where…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…
Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field…
Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…
Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators…