# Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification

arXiv: https://arxiv.org/abs/2304.06349 · HTML: https://mlsanity.com/paper/2304.06349/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [Deep Convolutional Networks in System Identification](https://mlsanity.com/paper/1909.01730/) (2019)
- [Model structures and fitting criteria for system identification with neural networks](https://mlsanity.com/paper/1911.13034/) (2019)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [Sparse Bayesian Deep Learning for Dynamic System Identification](https://mlsanity.com/paper/2107.12910/) (2021)
- [NARX Identification using Derivative-Based Regularized Neural Networks](https://mlsanity.com/paper/2204.05892/) (2022)

## Built on by (most cited first, 1 of 1)

- [Observability conditions for neural state-space models with eigenvalues and their roots of unity](https://mlsanity.com/paper/2504.15758/) (2025)

## Abstract (arXiv)

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the predictive uncertainty of deep-learning models describing non-linear dynamical systems are very limited to date. This paper is aimed at filling this gap and presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs through approximate inference techniques. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime, where predictions cannot be trusted.