Introducing Interval Neural Networks for Uncertainty-Aware System Identification

2025-04-26

AI Summary

Traditional linear models in system identification (SysID) suffer from limited representational capacity, while deep learning approaches lack rigorous uncertainty quantification (UQ). Method: This paper proposes a non-probabilistic Interval Neural Network (INN) framework that transforms pre-trained neural networks into interval-valued models and performs end-to-end interval arithmetic—enabling guaranteed prediction intervals without probabilistic assumptions. It introduces the novel concept of “elasticity” to characterize uncertainty sources and designs two SysID-specific architectures: Interval LSTM (ILSTM) and Interval Neural ODE (INODE), grounded in interval arithmetic, UQ-aware loss functions, and constrained interval-parameter optimization. Contribution/Results: Experiments across diverse dynamical systems demonstrate that ILSTM and INODE significantly improve both coverage and calibration of predictive intervals, achieving a favorable trade-off between high accuracy and strong reliability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

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.

Problem

• Develop Interval Neural Networks for uncertainty-aware system identification
• Address lack of uncertainty quantification in deep learning models
• Extend LSTM and Neural ODEs to interval-based architectures

Innovation

• Interval Neural Networks for uncertainty quantification
• Transforms pre-trained parameters into interval-valued ones
• Extends LSTM and Neural ODEs to interval versions