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Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by…

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…

Machine-learned interatomic potentials (MLPs) provide near density functional theory (DFT) accuracy at reduced computational cost, but their reliability depends on representative training data and often deteriorates in transition-state…

Multi-task/Multi-output learning seeks to exploit correlation among tasks to enhance performance over learning or solving each task independently. In this paper, we investigate this problem in the context of Gaussian Processes (GPs) and…

We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Laplacian constructed from the low-fidelity data is used to…

Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive…

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…

We study the average case performance of multi-task Gaussian process (GP) regression as captured in the learning curve, i.e. the average Bayes error for a chosen task versus the total number of examples $n$ for all tasks. For GP covariances…

We introduce interatomic potentials for tungsten in the bcc crystal phase and its defects within the Gaussian Approximation Potential (GAP) framework, fitted to a database of first principles density functional theory (DFT) calculations. We…

We present MOGPTK, a Python package for multi-channel data modelling using Gaussian processes (GP). The aim of this toolkit is to make multi-output GP (MOGP) models accessible to researchers, data scientists, and practitioners alike. MOGPTK…

Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To maintain tractability,…

The goal of the present work is to obtain accurate potential energy surfaces (PES) for high-dimensional molecular systems with a small number of ${\it ab}$ ${\it initio}$ calculations in a system-agnostic way. We use probabilistic modeling…

Accurate on-board capacity estimation is of critical importance in lithium-ion battery applications. Battery charging/discharging often occurs under a constant current load, and hence voltage vs. time measurements under this condition may…

Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…

A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve…

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

We propose a new scalable framework for spatio-temporal data fusion with multi-fidelity Gaussian processes (MFGPs) that enables fully likelihood-based inference for both stationary and non-stationary fidelity integration. The framework is…

Soft porous crystals are flexible metal-organic frameworks that respond to physical stimuli such as temperature, pressure, and gas adsorption by large changes in their structure and unit cell volume. While they have attracted a lot of…

In this paper, we propose a selective sampling procedure to preferentially evaluate a potential energy surface (PES) in a part of the configuration space governing a physical property of interest. The proposed sampling procedure is based on…

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…