Related papers: Bayesian learning with Gaussian processes for low-…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
The key idea of Bayesian optimization is replacing an expensive target function with a cheap surrogate model. By selection of an acquisition function for Bayesian optimization, we trade off between exploration and exploitation. The…
Bayesian Optimization is a popular approach for optimizing expensive black-box functions. Its key idea is to use a surrogate model to approximate the objective and, importantly, quantify the associated uncertainty that allows a sequential…
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…
Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…
Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry encounters formidable computational barriers. These bottlenecks are magnified for modeling data with many…
This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series. Using an experimental design of the low-and high-fidelity code levels, an original Gaussian process…
The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…
Data-driven model reduction methods provide a nonintrusive way of constructing computationally efficient surrogates of high-fidelity models for real-time control of soft robots. This work leverages the Lagrangian nature of the model…
This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…
A key requirement for the current generation of artificial decision-makers is that they should adapt well to changes in unexpected situations. This paper addresses the situation in which an AI for aerial dog fighting, with tunable…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
This paper deals with the problem of adaptive output regulation for multivariable nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. The approach builds on the recently proposed adaptive internal…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…
We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method…
Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…