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Engineering disciplines often rely on extensive simulations to ensure that structures are designed to withstand harsh conditions while avoiding over-engineering for unlikely scenarios. Assessments such as Serviceability Limit State (SLS)…

With the digitalization of power grids, physical equations become insufficient to describe the network's behavior, and realistic but time-consuming simulators must be used. Numerical experiments, such as safety validation, that involve…

Surrogate models are often used to replace costly-to-evaluate complex coastal codes to achieve substantial computational savings. In many of those models, the hydrometeorological forcing conditions (inputs) or flood events (outputs) are…

Several applications such as nuclear forensics, nuclear fuel cycle simulations and sensitivity analysis require methods to quickly compute spent fuel nuclide compositions for various irradiation histories. Traditionally, this has been done…

This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well…

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

We provide a survey of nonstationary surrogate models which utilize Gaussian processes (GPs) or variations thereof, including nonstationary kernel adaptations, partition and local GPs, and spatial warpings through deep Gaussian processes.…

With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring…

Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples…

Stiff ordinary differential equations (ODEs) play an important role in many scientific and engineering applications. Often, the dependence of the solution of the ODE on additional parameters is of interest, e.g.\ when dealing with…

Deep Gaussian processes (DGPs) are popular surrogate models for complex nonstationary computer experiments. DGPs use one or more latent Gaussian processes (GPs) to warp the input space into a plausibly stationary regime, then use typical GP…

Obtaining accurate estimates of satellite drag coefficients in low Earth orbit is a crucial component in positioning and collision avoidance. Simulators can produce accurate estimates, but their computational expense is much too large for…

Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with…

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates…

Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations. A particular focus is on the regime where only a small amount of training data is…