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Artificial neural network (ANN) potentials enable highly accurate atomistic simulations of complex materials at unprecedented scales. Despite their promise, training ANN potentials to represent intricate potential energy surfaces (PES) with…

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

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…

Quantifying uncertainties in physical or engineering systems often requires a large number of simulations of the underlying computer models that are computationally intensive. Emulators or surrogate models are often used to accelerate the…

Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI)…

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…

We consider adapting a canonical computer model calibration apparatus, involving coupled Gaussian process (GP) emulators, to a computer experiment simulating radiative shock hydrodynamics that is orders of magnitude larger than what can…

We develop a non-linear semi-parametric Gaussian process model to estimate periods of Miras with sparsely-sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes.…

Lost circulation remains a major and costly challenge in drilling operations, often resulting in wellbore instability, stuck pipe, and extended non-productive time. Accurate prediction of fluid loss is therefore essential for improving…

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…

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…

An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…

Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…

Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic…

An understanding of how input parameter uncertainty in the numerical simulation of physical models leads to simulation output uncertainty is a challenging task. Common methods for quantifying output uncertainty, such as performing a grid or…

Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios,…

Efficient and accurate simulations of the reionization epoch are crucial to exploring the vast uncharted parameter space that will soon be constrained by measurements of the 21 cm power spectrum. One of these parameters, $R_{\rm max}$, is…