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Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
Longitudinal data are important in numerous fields, such as healthcare, sociology and seismology, but real-world datasets present notable challenges for practitioners because they can be high-dimensional, contain structured missingness…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…
Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have…
High-fidelity simulations and physical experiments are essential for engineering analysis and design, yet their high cost often makes two critical tasks--global sensitivity analysis (GSA) and optimization--prohibitively expensive. This…
To validate the safety of automated vehicles (AV), scenario-based testing aims to systematically describe driving scenarios an AV might encounter. In this process, continuous inputs such as velocities result in an infinite number of…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
The analysis of variance (ANOVA) decomposition offers a systematic method to understand the interaction effects that contribute to a specific decision output. In this paper we introduce Neural-ANOVA, an approach to decompose neural networks…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We design a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements. The complex process is model-free. That is, we do not have…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
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…
The global sensitivity analysis of time-dependent processes requires history-aware approaches. We develop for that purpose a variance-based method that leverages the correlation structure of the problems under study and employs surrogate…
Causal inference with observational studies often suffers from unmeasured confounding, yielding biased estimators based on the unconfoundedness assumption. Sensitivity analysis assesses how the causal conclusions change with respect to…
The presented paper tackles the problem of modeling an unknown function, and its first $r-1$ derivatives, out of scattered and poor-quality data. The considered setting embraces a large number of use cases addressed in the literature and…
The transition from non-renewable to renewable energies represents a global societal challenge, and developing a sustainable energy portfolio is an especially daunting task for developing countries where little to no information is…
Simulations are becoming ever more common as a tool for designing complex products. Sensitivity analysis techniques can be applied to these simulations to gain insight, or to reduce the complexity of the problem at hand. However, these…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…