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Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of…

Hyper-parameter optimization remains as the core issue of Gaussian process (GP) for machine learning nowadays. The benchmark method using maximum likelihood (ML) estimation and gradient descent (GD) is impractical for processing big data…

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

Quantum computing technology has the potential to revolutionize the simulation of materials and molecules in the near future. A primary challenge in achieving near-term quantum advantage is effectively mitigating the noise effects inherent…

Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian…

Corrosion poses a significant challenge to the performance of aluminum alloys, particularly in marine environments. This study investigates the application of machine learning (ML) algorithms to predict and optimize corrosion resistance,…

Retinal prostheses restore vision by electrically stimulating surviving neurons, but calibrating perceptual thresholds (i.e., the minimum stimulus intensity required for perception) remains a time-intensive challenge, especially for…

When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in…

Spectral methods employing non-standard polynomial bases, such as M\"untz polynomials, have proven effective for accurately solving problems with solutions exhibiting low regularity, notably including sub-diffusion equations. However, due…

Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…

Accurate channel estimation with low pilot overhead and computational complexity is key to efficiently utilizing multi-antenna wireless systems. Motivated by the evolution from purely statistical descriptions toward physics- and…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise…

Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains. Such applications have two key features: (i) they…

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their…

This dissertation introduces measurement-based performance modeling and prediction techniques for dense linear algebra algorithms. As a core principle, these techniques avoid executions of such algorithms entirely, and instead predict their…

The robustness of the kernel recursive least square (KRLS) algorithm has recently been improved by combining them with more robust information-theoretic learning criteria, such as minimum error entropy (MEE) and generalized MEE (GMEE),…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…