Uncertainty Quantification

An Accelerated Course with Advanced Applications in Computational Engineering

  • Christian Soize

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 47)

About this book


This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. 

Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. <

This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.


High Stochastic Dimension Maximum Entropy Principle MCMC Methods Model Uncertainties Model-parameter Uncertainties Non-Gaussian Random Fields Nonparametric Uncertainties Polynomial Chaos Expansion Random Matrices Robust Design Statistical Inverse Problems Stochastic Reduced-order Computational Models

Authors and affiliations

  • Christian Soize
    • 1
  1. 1.Laboratoire Modélisation et Simulation Multi-Echelle (MSME)Université Paris-Est Marne-la-Vallée (UPEM)Marne-la-ValléeFrance

Bibliographic information