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Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…

Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar,…

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…

Satellite-based positioning system such as GPS often suffers from large amount of noise that degrades the positioning accuracy dramatically especially in real-time applications. In this work, we consider a data-mining approach to enhance…

Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications,…

The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…

Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…

The Gaussian Effective Potential (GEP) is shown to be a useful variational tool for the study of the magnetic properties of strongly correlated electronic systems. The GEP is derived for a single band Hubbard model on a two-dimensional…

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…

Bayesian hyperparameter optimization relies heavily on Gaussian Process (GP) surrogates, due to robust distributional posteriors and strong performance on limited training samples. GPs however underperform in categorical hyperparameter…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by…

Excessive loads near wounds produce pathological scarring and other complications. Presently, stress cannot easily be measured by surgeons in the operating room. Instead, surgeons rely on intuition and experience. Predictive computational…

Gaussian process (GP) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs…

Superhard materials with good fracture toughness have found wide industrial applications, which necessitates the development of accurate hardness and fracture toughness models for efficient materials design. Although several macroscopic…

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…

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,…

Edge transport barriers (ETBs) in magnetically confined fusion plasmas, commonly known as pedestals, play a crucial role in achieving high confinement plasmas. However, their defining characteristic, a steep rise in plasma pressure over…

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…