Interval Neural Networks for Uncertainty-Aware System Identification
System identification (SysID) is fundamental in understanding dynamic systems using data-driven models. Conventional SysID methods have predominantly relied on linear models, which may fail to effectively capture the complexities inherent in nonlinear systems. The advent of deep learning (DL) techniques offers enhanced capabilities for modeling these nonlinear dynamics, thus presenting a powerful alternative. However, DL models often lack mechanisms for quantifying uncertainty, an omission that can compromise the reliability and safety of their predictions. To address this critical barrier, the paper introduces Interval Neural Networks (INNs) for enhanced uncertainty quantification (UQ) in SysID tasks.
The central innovation of this paper is the transformation of the learnable parameters (LPs) of a neural network into interval-valued LPs, eliminating the dependence on probabilistic assumptions. Instead of assuming predefined distributions for uncertainty modeling, the proposed INNs leverage interval arithmetic to generate prediction intervals (PIs), ensuring effective coverage of target outcomes. This strategy provides a formal framework for integrating UQ into neural networks, particularly Long Short-Term Memory (LSTM) networks and Neural Ordinary Differential Equations (NODEs), which are common architectures in SysID applications.
Methodology and Implementation
The methodology revolves around constructing INNs by converting the LPs of pre-trained neural networks into interval parameters. This transformation is executed without necessitating probabilistic assumptions, making the approach flexible and broadly applicable across different types of SysID tasks. By embracing interval arithmetic, these networks can produce PIs that offer quantifiable confidence in the predictions.
Two novel architectures are proposed: Interval LSTM (ILSTM) and Interval NODE (INODE). The introduction of these architectures is supported by the mathematical foundations required for their application in SysID. The training process incorporates a deep learning framework equipped with a UQ loss function designed to balance the trade-offs between PI coverage and precision.
Experimental Validation
The paper empirically validates the efficacy of ILSTM and INODE via multiple SysID experiments. The models are tested against benchmark datasets that span various application domains, evaluating their ability to capture uncertainty effectively. The results, characterized by strong numerical performance metrics, demonstrate the robustness and reliability of the proposed interval networks in generating PIs.
Among the configurations assessed, INODE-2 and ILSTM-2 showcased superior UQ capabilities, achieving target coverage with considerable precision. A detailed elasticity analysis further reveals how specific network parameters contribute to uncertainty quantification. Such insights underline the potential for these models in not only predicting outcomes but also offering transparency regarding the uncertainty inherent in their predictions.
Implications and Future Directions
The introduction of INNs represents a significant advancement in the practice of system identification, providing a structured approach to integrating uncertainty into DL models. The implications extend both theoretically, offering new pathways for model development, and practically, enhancing the reliability and safety of predictions in real-world applications. By enabling robust uncertainty quantification, these models promote confidence in deploying DL solutions across domains where understanding the reliability of predictions is as critical as the predictions themselves.
Future research can aim to extend the interval design to other network architectures, such as convolutional neural networks (CNNs), thereby broadening their applicability. Additionally, exploring real-time SysID tasks and advancing interpretability in UQ are promising directions that could further enrich the field. Overall, the systematic introduction and evaluation of INNs marks a substantial step in advancing reliable and uncertainty-aware modeling practices for dynamic systems.
