Related papers: Cross-Validation Based Adaptive Sampling for Multi…

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

We introduce a simple and scalable method for training Gaussian process (GP) models that exploits cross-validation and nearest neighbor truncation. To accommodate binary and multi-class classification we leverage P\`olya-Gamma auxiliary…

Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

A simple and widely adopted approach to extend Gaussian processes (GPs) to multiple outputs is to model each output as a linear combination of a collection of shared, unobserved latent GPs. An issue with this approach is choosing the number…

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…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

With the growing application of spatial predictive modeling in ecology, the question of how to appropriately evaluate the resulting maps has gained increasing attention. While there is consensus that map accuracy is ideally estimated using…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it…

Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

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…

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this…

We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

Unpredictable and complex aerodynamic effects pose significant challenges to achieving precise flight control, such as the downwash effect from upper vehicles to lower ones. Conventional methods often struggle to accurately model these…

The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full…