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The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…

Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…

We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure…

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's…

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…

We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Deep geological repositories are critical for the long-term storage of hazardous materials, where understanding the mechanical behavior of emplacement drifts is essential for safety assurance. This study presents a surrogate modeling…

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Sparse variational Gaussian process (SVGP) methods are a common choice for non-conjugate Gaussian process inference because of their computational benefits. In this paper, we improve their computational efficiency by using a dual…

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…

Predicting the labels of graph-structured data is crucial in scientific applications and is often achieved using graph neural networks (GNNs). However, when data is scarce, GNNs suffer from overfitting, leading to poor performance.…

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…

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…

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose…

Gaussian processes (GPs) are highly flexible function estimators used for geospatial analysis, nonparametric regression, and machine learning, but they are computationally infeasible for large datasets. Vecchia approximations of GPs have…

Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…

Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…