# What Uncertainties Do We Need for Dynamical Systems?

arXiv: https://arxiv.org/abs/2606.11988 · HTML: https://mlsanity.com/paper/2606.11988/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Stable Recurrent Models](https://mlsanity.com/paper/1805.10369/) (2018)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [Sources of Uncertainty in Supervised Machine Learning -- A Statisticians' View](https://mlsanity.com/paper/2305.16703/) (2023)

## Abstract (arXiv)

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.