Introducing Interval Neural Networks for Uncertainty-Aware System Identification

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.