A Survey on Uncertainty Quantification in Dynamical Systems

There is uncertainty in various domains, requiring a robust understanding and quantification in order to make informed decisions. This article presents a comprehensive discussion of uncertainty quantification (UQ) in dynamical systems. Beginning with an overview, we examine the multifaceted nature of uncertainty and the challenges in its modeling and analysis. Identifying key sources that shape uncertainty is essential for accurate quantification. Whether models are deterministic or stochastic, statistical inference remains crucial for robust modeling and decision-making in UQ. This article introduces a state-of-the-art classification of UQ methods, comprising two fundamental categories: 1) forward propagation techniques and 2) backward propagation techniques, each designed to address specific challenges in UQ. By equipping readers with essential tools for managing uncertainty, this article aims to broaden the application of UQ across engineering, physics, technology, and healthcare.