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There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as well as the model inadequacy. However, the application of…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Oilfield development related decisions are made using reservoir simulation-based optimization study in which different production scenarios and well controls are compared. Such simulations are computationally expensive and so surrogate…

Shrinkage prior has gained great successes in many data analysis, however, its applications mostly focus on the Bayesian modeling of sparse parameters. In this work, we will apply Bayesian shrinkage to model high dimensional parameter that…

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…

Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this…

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…

Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, the loss ignores misspecification, where models are imperfect. Parameter uncertainties from Bayesian…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

Finite temperature disordered solid solutions and magnetic materials are difficult to study directly using first principles calculations, due to the large unit cells and many independent samples that are required. In this work, we develop a…

Fatigue crack growth is one of the most common types of deterioration in metal structures with significant implications on their reliability. Recent advances in Structural Health Monitoring (SHM) have motivated the use of structural…

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

Computationally-guided material discovery is being increasingly employed using a descriptor-based screening through the calculation of a few properties of interest. A precise understanding of the uncertainty associated with first principles…

Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

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…

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…

To improve the theoretical prediction power for synthesizing superheavy elements beyond Og, a Bayesian uncertainty quantification method is employed to evaluate the uncertainty of the calculated evaporation residue cross sections (ERCS) for…