Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspective
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909848772280320 |
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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 |
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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 |