# Learning Surrogate LPV State-Space Models with Uncertainty Quantification

arXiv: https://arxiv.org/abs/2603.29532 · HTML: https://mlsanity.com/paper/2603.29532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [A Tutorial on Learning With Bayesian Networks](https://mlsanity.com/paper/2002.00269/) (2020)
- [NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators](https://mlsanity.com/paper/2208.11866/) (2022)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [On the Initialization of Nonlinear LFR Model Identification with the Best Linear Approximation](https://mlsanity.com/paper/2004.05040/) (2020)
- [Variational System Identification for Nonlinear State-Space Models](https://mlsanity.com/paper/2012.05072/) (2020)
- [Learning-based model augmentation with LFRs](https://mlsanity.com/paper/2404.01901/) (2024)
- [Efficient identification of linear, parameter-varying, and nonlinear systems with noise models](https://mlsanity.com/paper/2504.11982/) (2025)
- [Adaptive Uncertainty Quantification for Scenario-based Control Using Meta-learning of Bayesian Neural Networks](https://mlsanity.com/paper/2407.14492/) (2024)

## Abstract (arXiv)

The Linear Parameter-Varying (LPV) framework enables the construction of surrogate models of complex nonlinear and high-dimensional systems, facilitating efficient stability and performance analysis together with controller design. Despite significant advances in data-driven LPV modelling, existing approaches do not quantify the uncertainty of the obtained LPV models. Consequently, assessing model reliability for analysis and control or detecting operation outside the training regime requires extensive validation and user expertise. This paper proposes a Bayesian approach for the joint estimation of LPV state-space models, including their scheduling map, together with characterization of the model uncertainty and confidence bounds on the predicted model response directly from input-output data. Both aleatoric uncertainty due to measurement noise and epistemic uncertainty arising from limited training data and structural bias are considered. The resulting model preserves the LPV structure required for controller synthesis while enabling computationally efficient simulation and uncertainty propagation. The approach is demonstrated on the surrogate modelling of a two-dimensional nonlinear interconnection of mass-spring-damper systems.