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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…
Finite element model updating utilizing frequency response functions as inputs is an important procedure in structural analysis, design and control. This paper presents a highly efficient framework that is built upon Gaussian process…
The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility…
In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias &…
While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…
Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…
We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…
We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real…
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…
Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…
Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability,…
Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes…
Due to the increasing complexity of technical systems, accurate first principle models can often not be obtained. Supervised machine learning can mitigate this issue by inferring models from measurement data. Gaussian process regression is…
Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Understanding which concepts models can and cannot represent has been fundamental to many tasks: from effective and responsible use of models to detecting out of distribution data. We introduce Gaussian process probes (GPP), a unified and…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…