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In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…
Characterizing the interior structure of exoplanets is an inverse problem often solved using Bayesian inference, but this approach is hampered by the high computational cost of planetary structure models. To overcome this barrier, we…
In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear…
Aerodynamic shape optimization in industry still faces challenges related to robustness and scalability. This aspect becomes crucial for advanced optimizations that rely on expensive high-fidelity flow solvers, where computational budget…
In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
Markov chain Monte Carlo (MCMC) sampling of posterior distributions arising in Bayesian inverse problems is challenging when evaluations of the forward model are computationally expensive. Replacing the forward model with a low-cost,…
Polynomial Chaos Expansions (PCEs) are widely recognized for their efficient computational performance in surrogate modeling. Yet, a robust framework to quantify local model errors is still lacking. While the local uncertainty of PCE…
In engineering design and scientific computing, computational cost and predictive accuracy are intrinsically coupled. High-fidelity simulations provide accurate predictions but at substantial computational costs, while lower-fidelity…
This paper deals with surrogate modelling of a computer code output in a hierarchical multi-fidelity context, i.e., when the output can be evaluated at different levels of accuracy and computational cost. Using observations of the output at…
Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…
Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty…
Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in…
Multifidelity surrogate modelling combines data of varying accuracy and cost from different sources. It strategically uses low-fidelity models for rapid evaluations, saving computational resources, and high-fidelity models for detailed…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
Stochastic inverse problems are generally solved by some form of finite sampling of a space of uncertain parameters. For computationally expensive models, surrogate response surfaces are often employed to increase the number of samples used…
Implementations of Markov chain Monte Carlo (MCMC) methods need to confront two fundamental challenges: accurate representation of prior information and efficient evaluation of likelihoods. Principal component analysis (PCA) and related…
Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can…
For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…
Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many…