Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners

TL;DR

This tutorial introduces beginners to uncertainty quantification (UQ) using simple examples, covering its principles, applications in dynamical systems, data assimilation, diagnostics, and modeling, with accessible code resources.

Contribution

It provides an accessible, beginner-friendly introduction to UQ concepts and applications, using simple examples and available code in MATLAB and Python.

Findings

UQ is essential for understanding uncertainties in complex systems

Simple examples effectively illustrate UQ principles

Accessible tutorials facilitate learning for undergraduates

Abstract

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.