This paper provides a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more in this area. It exploits many very simple examples, which are understandable to undergraduates, to present the ideas of UQ. Topics include characterizing uncertainties using information theory, UQ in linear and nonlinear dynamical systems, UQ via data assimilation, the role of uncertainty in diagnostics, and UQ in advancing efficient modeling. The surprisingly simple examples in each topic explain why and how UQ is essential. Both MATLAB and Python codes are made available for these simple examples.
@article{arxiv.2408.01823,
title = {Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners},
author = {Nan Chen and Stephen Wiggins and Marios Andreou},
journal= {arXiv preprint arXiv:2408.01823},
year = {2025}
}
Comments
33 pages (Main Text pp. 1--12; Supplementary Document pp. 13--33), 15 figures (7 in Main Text, 8 in Supplementary Document), 1 table (in Supplementary Document). Published in the Notices of the American Mathematical Society. The code to the examples in the supplementary document can be found in https://github.com/marandmath/UQ_tutorial_code