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