What Uncertainties Do We Need for Dynamical Systems?

2026-06-10

AI Summary

This work addresses the frequent conflation of aleatoric (inherent randomness) and epistemic (modeling ignorance) uncertainties in dynamic systems, which often lacks task-aware differentiation and adaptation. For the first time in the context of dynamic systems, this study systematically clarifies the distinct origins and characteristics of these two uncertainty types and elucidates how their modeling objectives diverge across different tasks. Building upon probabilistic modeling and Bayesian inference within a dynamic systems framework, the paper proposes a task-oriented approach to uncertainty representation and quantification. It articulates key modeling principles that explicitly align uncertainty treatment with downstream objectives, thereby establishing a rigorous theoretical foundation for robust prediction, control, and decision-making under uncertainty.

Abstract

The distinction between aleatoric and epistemic uncertainty has received considerable attention in machine learning research, mainly in the context of supervised learning but also in other settings such as generative modeling. In this paper, we offer a machine learning perspective on uncertainty modeling for dynamical systems, which has been studied much less so far. In particular, we ask: what uncertainties do we need for dynamical systems? We discuss sources of uncertainty, clarify their nature (aleatoric or epistemic), and consider how the objectives of representing and quantifying uncertainty vary across different tasks.

Problem

• uncertainty
• dynamical systems
• aleatoric uncertainty
• epistemic uncertainty
• machine learning

Innovation

• dynamical systems
• uncertainty quantification
• aleatoric uncertainty
• epistemic uncertainty
• machine learning