# Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identification

arXiv: https://arxiv.org/abs/2605.11460 · HTML: https://mlsanity.com/paper/2605.11460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 22 of 22)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [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)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [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)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [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)
- [Optimal Uncertainty-guided Neural Network Training](https://mlsanity.com/paper/1912.12761/) (2019)
- [A Toolbox for Fast Interval Arithmetic in numpy with an Application to Formal Verification of Neural Network Controlled Systems](https://mlsanity.com/paper/2306.15340/) (2023)
- [Deep Learning of Dynamic Systems using System Identification Toolbox(TM)](https://mlsanity.com/paper/2409.07642/) (2024)
- [dynoGP: Deep Gaussian Processes for dynamic system identification](https://mlsanity.com/paper/2502.05620/) (2025)
- [Introducing Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2504.18845/) (2025)
- [SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems](https://mlsanity.com/paper/2604.14879/) (2026)

## Abstract (arXiv)

System identification (SysID) is critical for modeling dynamical systems from experimental data, yet traditional approaches often fail to capture nonlinear behaviors. While deep learning offers powerful tools for modeling such dynamics, incorporating uncertainty quantification is essential to ensure reliable predictions. This paper presents a systematic framework for constructing and training interval Neural Networks (INNs) for uncertainty-aware SysID. By extending crisp neural networks into interval counterparts, we develop Interval LSTM and NODE models that propagate uncertainty through interval arithmetic without probabilistic assumptions. This design allows them to represent uncertainty and produce prediction intervals. For training, we propose two strategies: Cascade INN (C-INN), a two-stage approach converting a trained crisp NN into an INN, and Joint INN (J-INN), a one-stage framework jointly optimizing prediction accuracy and interval precision. Both strategies employ uncertainty-aware loss functions and parameterization tricks to ensure reliable learning. Comprehensive experiments on multiple SysID datasets demonstrate the effectiveness of both approaches and benchmark their performance against well-established uncertainty-aware baselines: C-INN achieves superior point prediction accuracy, whereas J-INN yields more accurate and better-calibrated prediction intervals. Furthermore, to reveal how uncertainty is represented across model parameters, the concept of channel-wise elasticity is introduced, which is used to identify distinct patterns across the two training strategies. The results of this study demonstrate that the proposed framework effectively integrates deep learning with uncertainty-aware modeling.