Related papers: Safe Real-Time Optimization using Multi-Fidelity G…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations. Multi-fidelity methods provide a solution by chaining models in a…
Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may…
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…
An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
To assess the possibility of evacuating a building in case of a fire, a standard method consists in simulating the propagation of fire, using finite difference methods and takes into account the random behavior of the fire, so that the…
Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to…
Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…
Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression. The methodologies rely chiefly on the method of maximizing the…