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

Fuente: arXiv
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Main Authors: De Carli, Stefano, Previtali, Davide, Pitturelli, Leandro, Mazzoleni, Mirko, Ferramosca, Antonio, Previdi, Fabio
Format: Preprint
Published: 2025
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author De Carli, Stefano
Previtali, Davide
Pitturelli, Leandro
Mazzoleni, Mirko
Ferramosca, Antonio
Previdi, Fabio
author_facet De Carli, Stefano
Previtali, Davide
Pitturelli, Leandro
Mazzoleni, Mirko
Ferramosca, Antonio
Previdi, Fabio
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_11553
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspective
De Carli, Stefano
Previtali, Davide
Pitturelli, Leandro
Mazzoleni, Mirko
Ferramosca, Antonio
Previdi, Fabio
Optimization and Control
Machine Learning
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.
title Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspective
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2503.11553