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

arXiv: https://arxiv.org/abs/2503.11553 · HTML: https://mlsanity.com/paper/2503.11553/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 28 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 2 of 2)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [On the stability properties of Gated Recurrent Units neural networks](https://mlsanity.com/paper/2011.06806/) (2020)

## Built on by (most cited first, 1 of 1)

- [Integrating Biological-Informed Recurrent Neural Networks for Glucose-Insulin Dynamics Modeling](https://mlsanity.com/paper/2503.19158/) (2025)

## Abstract (arXiv)

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∞) for Long Short-Term Memory (LSTM) networks. The obtained condition depends on fewer network parameters compared to prior works. A ISS∞-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∞-promoted LSTM outperforms both a physics-based model and an ISS∞-promoted Gated Recurrent Unit (GRU) network while also surpassing non-ISS∞-promoted LSTM and GRU RNNs.