arXiv subjects

Stefano De Carli

Publications and source records attributed to Stefano De Carli.

4 recordsLinked to original sources

arXiv2026

Stability properties of Minimal Gated Unit neural networks

In this work, we address the need for efficient and formally stable Recurrent Neural Networks (RNNs) in environments with limited computational resources by analyzing the stability of the Minimal Gated Unit (MGU) network, a lightweight alternative to common gated RNNs used in system identification. We derive sufficient parametric conditions for the MGU network's input-to-state stability and incremental input-to-state stability properties. These conditions enable a-posteriori validation of model stability and form the basis for novel stability-promoting training methodologies, including a warm-start of the network's parameters and a projected gradient-based optimization scheme, both of which are presented in this work. Comparative evaluation, including robustness analysis and validation on synthetic and real-world data (i.e., the Silverbox benchmark), demonstrates that the minimal gated unit network successfully combines formal stability guarantees with superior parameter efficiency and faster inference times compared to other state-of-the-art recurrent neural networks, while maintaining comparable and satisfactory accuracy. Notably, the results attained on the Silverbox benchmark illustrate that the stable MGU network effectively captures the system dynamics, whereas other stable RNNs fail to converge to a reliable model.

math.OC↗

arXiv2026

Integrating Biological-Informed Recurrent Neural Networks for Glucose-Insulin Dynamics Modeling

Type 1 Diabetes (T1D) management is a complex task due to many variability factors. Artificial Pancreas (AP) systems have alleviated patient burden by automating insulin delivery through advanced control algorithms. However, the effectiveness of these systems depends on accurate modeling of glucose-insulin dynamics, which traditional mathematical models often fail to capture due to their inability to adapt to patient-specific variations. This study introduces a Biological-Informed Recurrent Neural Network (BIRNN) framework to address these limitations. The BIRNN leverages a Gated Recurrent Units (GRU) architecture augmented with physics-informed loss functions that embed physiological constraints, ensuring a balance between predictive accuracy and consistency with biological principles. The framework is validated using the commercial UVA/Padova simulator, outperforming traditional linear models in glucose prediction accuracy and reconstruction of unmeasured states, even under circadian variations in insulin sensitivity. The results demonstrate the potential of BIRNN for personalized glucose regulation and future adaptive control strategies in AP systems.

cs.LG↗

arXiv2026

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

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.

math.OC↗

arXiv2026

Chaos-Free Networks are Stable Recurrent Neural Networks

Gated Recurrent Neural Networks (RNNs) are widely used for nonlinear system identification due to their high accuracy, although they often exhibit complex, chaotic dynamics that are difficult to analyze. This paper investigates the system-theoretic properties of the Chaos-Free Network (CFN), an architecture originally proposed to eliminate the chaotic behavior found in standard gated RNNs. First, we formally prove that the CFN satisfies Input-to-State Stability (ISS) by design. However, we demonstrate that the CFN architecture does not intrinsically guarantee Incremental ISS (delta-ISS), as ensuring this property relies on specific parametric constraints. To address this, we introduce the Decoupled-Gate Network (DGN), a novel structural variant of the CFN that removes internal state connections in the gating mechanisms. Finally, we prove that the DGN unconditionally satisfies the delta-ISS property, providing an incrementally stable architecture for identifying nonlinear dynamical systems without requiring complex network training modifications. Numerical results confirm that the DGN maintains the modeling capabilities of standard architectures while adhering to these rigorous stability guarantees.

math.OC↗