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Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…

This work presents a novel posterior inference method for models with intractable evidence and likelihood functions. Error-guided likelihood-free MCMC, or EG-LF-MCMC in short, has been developed for scientific applications, where a…

In computer chip manufacturing, the study of etch patterns on silicon wafers, or metrology, occurs on the nano-scale and is therefore subject to large variation from small, yet significant, perturbations in the manufacturing environment. An…

Science and engineering fields use computer simulation extensively. These simulations are often run at multiple levels of sophistication to balance accuracy and efficiency. Multi-fidelity surrogate modeling reduces the computational cost by…

Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…

Multi-fidelity (MF) modeling is a powerful statistical approach that can intelligently blend data from varied fidelity sources. This approach finds a compelling application in predicting melt pool geometry for laser-directed energy…

Materials design can be cast as an optimization problem with the goal of achieving desired properties, by varying material composition, microstructure morphology, and processing conditions. Existence of both qualitative and quantitative…

Model-based geostatistical design involves the selection of locations to collect data to minimise an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which,…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Bayesian optimization (BO) is increasingly employed in critical applications such as materials design and drug discovery. An increasingly popular strategy in BO is to forgo the sole reliance on high-fidelity data and instead use an ensemble…

Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…

Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional…

Modern aerospace guidance systems demand rigorous constraint satisfaction, optimal performance, and computational efficiency. Traditional analytical methods struggle to simultaneously satisfy these requirements. While data driven methods…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

Machine learning potentials (MLPs) have become an indispensable tool in large-scale atomistic simulations because of their ability to reproduce ab initio potential energy surfaces (PESs) very accurately at a fraction of computational cost.…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Cooperative online scalar field mapping is an important task for multi-robot systems. Gaussian process regression is widely used to construct a map that represents spatial information with confidence intervals. However, it is difficult to…

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centred auxiliary basis, which enables an accurate expansion of the all-electron density in…

For machine learning of interatomic potentials a scalable sparse Gaussian process regression formalism is introduced with a data-efficient on-the-fly adaptive sampling algorithm. With this approach, the computational cost is effectively…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…