Beyond prediction: Interval neural networks for uncertainty-aware system identification

System identification (SysID) is critical for modeling dynamical systems from experimental data, yet traditional approaches often fail to capture nonlinear behaviors while providing reliable confidence estimates. While Neural Networks (NNs) offer 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 NN (INNs) for uncertainty-aware SysID. By extending crisp neural networks into interval counterparts, we develop Interval LSTM and Interval 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 quality. Both strategies employ uncertainty-aware loss functions and parameterization techniques to ensure reliable learning. Comprehensive experiments on multiple SysID datasets and comparisons with well-established uncertainty-aware NN baselines demonstrate the effectiveness of both approaches. Specifically, C-INN achieves superior point prediction accuracy, whereas J-INN yields more accurate and better-calibrated prediction intervals. Among the proposed architectures, the INODE models consistently provide the best overall balance between predictive accuracy and uncertainty quantification. 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 reliable and interpretable uncertainty-aware modeling.