# Introducing Interval Neural Networks for Uncertainty-Aware System Identification

arXiv: https://arxiv.org/abs/2504.18845 · HTML: https://mlsanity.com/paper/2504.18845/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 26 Apr 2025.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Understanding Certified Training with Interval Bound Propagation](https://mlsanity.com/paper/2306.10426/) (2023)
- [Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression](https://mlsanity.com/paper/2109.08248/) (2021)
- [Neural Ordinary Differential Equations for Nonlinear System Identification](https://mlsanity.com/paper/2203.00120/) (2022)
- [Interval Neural Networks: Uncertainty Scores](https://mlsanity.com/paper/2003.11566/) (2020)
- [Enhancing Continuous Time Series Modelling with a Latent ODE-LSTM Approach](https://mlsanity.com/paper/2307.05126/) (2023)
- [Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise](https://mlsanity.com/paper/2406.03258/) (2024)

## Built on by (most cited first, 3 of 3)

- [Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification](https://mlsanity.com/paper/2510.24757/) (2025)
- [SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems](https://mlsanity.com/paper/2604.14879/) (2026)
- [Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2605.11460/) (2026)

## Abstract (arXiv)

System Identification (SysID) is crucial for modeling and understanding dynamical systems using experimental data. While traditional SysID methods emphasize linear models, their inability to fully capture nonlinear dynamics has driven the adoption of Deep Learning (DL) as a more powerful alternative. However, the lack of uncertainty quantification (UQ) in DL-based models poses challenges for reliability and safety, highlighting the necessity of incorporating UQ. This paper introduces a systematic framework for constructing and learning Interval Neural Networks (INNs) to perform UQ in SysID tasks. INNs are derived by transforming the learnable parameters (LPs) of pre-trained neural networks into interval-valued LPs without relying on probabilistic assumptions. By employing interval arithmetic throughout the network, INNs can generate Prediction Intervals (PIs) that capture target coverage effectively. We extend Long Short-Term Memory (LSTM) and Neural Ordinary Differential Equations (Neural ODEs) into Interval LSTM (ILSTM) and Interval NODE (INODE) architectures, providing the mathematical foundations for their application in SysID. To train INNs, we propose a DL framework that integrates a UQ loss function and parameterization tricks to handle constraints arising from interval LPs. We introduce novel concept "elasticity" for underlying uncertainty causes and validate ILSTM and INODE in SysID experiments, demonstrating their effectiveness.