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Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
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…
Multi-fidelity Gaussian process is a common approach to address the extensive computationally demanding algorithms such as optimization, calibration and uncertainty quantification. Adaptive sampling for multi-fidelity Gaussian process is a…
In latent variable models the parameter estimation can be implemented by using the joint or the marginal likelihood, based on independence or conditional independence assumptions. The same dilemma occurs within the Bayesian framework with…
Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of…
Multi-fidelity methods that use an ensemble of models to compute a Monte Carlo estimator of the expectation of a high-fidelity model can significantly reduce computational costs compared to single-model approaches. These methods use oracle…
Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an…
In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate…
We provide a collection of results on covariance expressions between Monte Carlo based multi-output mean, variance, and Sobol main effect variance estimators from an ensemble of models. These covariances can be used within multi-fidelity…
The recent growth in multi-fidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a…
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
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…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Mathematical models in computational physics contain uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds averaged Navier-Stokes (RANS) models, such as the…