The increasing availability of data, due to the adoption of low-cost industrial internet of things
technologies, coupled with increasing processing power from cloud computing, is fuelling …

The notion of uncertainty is of major importance in machine learning and constitutes a key
element of machine learning methodology. In line with the statistical tradition, uncertainty …

The recent decades have seen various attempts at accelerating the process of developing
materials targeted towards specific applications. The performance required for a particular …

This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …

Parameter studies are everywhere in computational science. Complex engineering
simulations must run several times with different inputs to effectively study the relationships …

In many fields, such as environmental risk assessment, agronomic system behavior,
aerospace engineering, and nuclear safety, mathematical models turned into computer code …

This book places data assimilation (DA) into the broader context of inverse problems and the
theory, methods, and algorithms that are used for their solution. It strives to provide a …

We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/
multiresolution method for PDEs with rough (L^∞) coefficients with rigorous a priori …

The objective of uncertainty quantification is to certify that a given physical, engineering or
economic system satisfies multiple safety conditions with high probability. A more ambitious …

Key questions that scientists and engineers typically want to address can be formulated in
terms of predictive science. Questions such as:" How well does my computational model …