On top of machine learning (ML) models, uncertainty quantification (UQ) functions as an
essential layer of safety assurance that could lead to more principled decision making by …

Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that
takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful …

Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to
describe phenomena and computational challenges that arise in high dimensions. These …

Constructing accurate and generalizable approximators (surrogate models) for complex
physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The …

A review of theoretical concepts and diverse applications of sparse representations and
compressive sampling (CS) approaches in engineering mechanics problems is provided …

Constructing surrogate models for uncertainty quantification (UQ) on complex partial
differential equations (PDEs) having inherently high-dimensional O (10 n), n≥ 2, stochastic …

Thanks to their versatility, ease of deployment, and high performance, surrogate models
have become staple tools in the arsenal of uncertainty quantification (UQ). From local …

In this work we introduce a manifold learning-based method for uncertainty quantification
(UQ) in systems describing complex spatiotemporal processes. Our first objective is to …

The computational cost of high-fidelity numerical models makes outer-loop analysis, which
requires repeated interrogation of the model such as uncertainty quantification …

Uncertainty quantification of engineering systems modeled by computationally intensive
numerical models remains a challenging task, despite the increase in computer power …