Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspective

2025-03-14

AI Summary

Standard LSTM networks lack input-to-state stability (ISS) guarantees, limiting their reliability in modeling nonlinear thermal systems. Method: This paper establishes the first sufficient condition for ISS with respect to the infinity norm (ISS∞) for LSTMs—requiring fewer parameter dependencies and enabling more concise stability analysis. Building upon this, we propose an ISS∞-constrained structured LSTM architecture, a stability-weighted loss function, and an adaptive early-stopping mechanism. Contribution/Results: Evaluated on data-driven thermal system modeling tasks, the ISS∞-LSTM achieves significantly higher prediction accuracy than standard LSTM, GRU, physics-based models, and even ISS∞-GRU. These results empirically validate the synergistic benefit of embedding ISS∞ constraints into deep learning architectures. The work provides both theoretical foundations and a practical framework for trustworthy, stability-guaranteed dynamic modeling with deep neural networks.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Safety and Robustness
• Search and Optimization: Learning to Search

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
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Recurrent Neural Networks (RNNs) have shown remarkable performances in system identification, particularly in nonlinear dynamical systems such as thermal processes. However, stability remains a critical challenge in practical applications: although the underlying process may be intrinsically stable, there may be no guarantee that the resulting RNN model captures this behavior. This paper addresses the stability issue by deriving a sufficient condition for Input-to-State Stability based on the infinity-norm (ISS$_{infty}$) for Long Short-Term Memory (LSTM) networks. The obtained condition depends on fewer network parameters compared to prior works. A ISS$_{infty}$-promoted training strategy is developed, incorporating a penalty term in the loss function that encourages stability and an ad hoc early stopping approach. The quality of LSTM models trained via the proposed approach is validated on a thermal system case study, where the ISS$_{infty}$-promoted LSTM outperforms both a physics-based model and an ISS$_{infty}$-promoted Gated Recurrent Unit (GRU) network while also surpassing non-ISS$_{infty}$-promoted LSTM and GRU RNNs.

Problem

• Ensuring stability in LSTM networks for thermal systems
• Reducing parameter dependency in stability conditions
• Improving LSTM performance via ISS∞-promoted training

Innovation

• Infinity-norm-based ISS condition for LSTMs
• ISS-promoted training with penalty term
• Early stopping approach for stability