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

2026-05-11

AI Summary

This work addresses the limitations of traditional system identification methods, which struggle to model nonlinear dynamics and lack reliable uncertainty quantification. For the first time, interval neural networks (INNs) are introduced to system identification, with two novel training strategies—Cascade INN (C-INN) and Joint INN (J-INN)—that integrate interval arithmetic, interval LSTM, interval neural ordinary differential equations, and an uncertainty-aware loss function. These approaches enable high-accuracy point predictions and well-calibrated prediction intervals without requiring probabilistic assumptions. Experimental results demonstrate that C-INN significantly improves point prediction accuracy, while J-INN yields more precise uncertainty intervals, outperforming state-of-the-art baselines. Furthermore, the concept of “channel elasticity” is introduced to elucidate the mechanism by which parameter-level uncertainty is represented within the model.

Abstract

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.

Problem

• system identification
• uncertainty quantification
• interval neural networks
• nonlinear dynamics
• prediction intervals

Innovation

• Interval Neural Networks
• Uncertainty Quantification
• System Identification
• Interval Arithmetic
• Channel-wise Elasticity