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Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and…

Background: Scatterometry is a fast, indirect and non-destructive optical method for quality control in the production of lithography masks. To solve the inverse problem in compliance with the upcoming need for improved accuracy, a…

Testing and evaluation are expensive but critical steps in the development of connected and automated vehicles (CAVs). In this paper, we develop an adaptive sampling framework to efficiently evaluate the accident rate of CAVs, particularly…

We address the challenge of constructing noise-robust surrogate models for quantities of interest (QoIs) arising from parametric partial differential equations (PDEs), using multi-fidelity collocation techniques; specifically, the…

Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on…

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a…

A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration,…

Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy…

Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

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…

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

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…

Standard Bayesian inference schemes are infeasible for inverse problems with computationally expensive forward models. A common solution is to replace the model with a cheaper surrogate. To avoid overconfident conclusions, it is essential…

Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…

In Bayesian phylogenetics, our goal is to estimate the posterior distribution over phylogenetic trees. Markov chain Monte Carlo methods are widely used to approximate the phylogenetic posterior distributions. For large-scale sequence data,…

The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to…

Multi-fidelity Kriging model is a promising technique in surrogate-based design as it can balance the model accuracy and cost of sample preparation by fusing low- and high-fidelity data. However, the cost for building a multi-fidelity…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

Approximate Bayesian Computation (ABC) methods often require extensive simulations, resulting in high computational costs. This paper focuses on multifidelity simulation models and proposes a pre-filtering hierarchical importance sampling…