Pneumatic Artificial Muscles (PAMs) are complex nonlinear systems characterized by hysteresis, making them challenging to model with classical system identification methods. While deep learning has emerged as a powerful tool for modeling nonlinear systems from data, purely neural networkbased models often lack interpretability and are prone to overfitting. To address these challenges, this study explores several hybrid approaches that combine analytical models with neural networks to model PAM behavior more effectively. The results demonstrate that hybrid models significantly outperform both purely analytical and black-box neural network models, particularly in terms of generalization and dynamic accuracy. Among the approaches, the Physics-Informed Neural Network (PINN) unsupervised model shows the most robust performance, capturing complex PAM dynamics while maintaining computational efficiency. These findings suggest that hybrid modeling is a promising and scalable solution for accurately representing the intricate behavior of PAMs.

Interpretability of neural networks (NNs) and their underlying theoretical behavior remain an open field of study even after the great success of their practical applications, particularly with the emergence of deep learning. In this work, NN2Poly is proposed: a theoretical approach to obtain an explicit polynomial model that provides an accurate representation of an already trained fully connected feed-forward artificial NN [a multilayer perceptron (MLP)]. This approach extends a previous idea proposed in the literature, which was limited to single hidden layer networks, to work with arbitrarily deep MLPs in both regression and classification tasks. NN2Poly uses a Taylor expansion on the activation function, at each layer, and then applies several combinatorial properties to calculate the coefficients of the desired polynomials. Discussion is presented on the main computational challenges of this method, and the way to overcome them by imposing certain constraints during the training phase. Finally, simulation experiments as well as applications to real tabular datasets are presented to demonstrate the effectiveness of the proposed method.

Abstract Hand gesture recognition and classification play a pivotal role in automating Human‐Computer Interaction (HCI) and have garnered substantial attention in research. In this study, the focus is placed on the application of gesture recognition in surgical settings to provide valuable feedback during medical training. A tool gesture classification system based on Deep Learning (DL) techniques is proposed, specifically employing a Long Short Term Memory (LSTM)‐based model with an attention mechanism. The research is structured in three key stages: data pre‐processing to eliminate outliers and smooth trajectories, addressing noise from surgical instrument data acquisition; data augmentation to overcome data scarcity by generating new trajectories through controlled spatial transformations; and the implementation and evaluation of the DL‐based classification strategy. The dataset used includes recordings from ten participants with varying surgical experience, covering three types of trajectories and involving both right and left arms. The proposed classifier, combined with the data augmentation strategy, is assessed for its effectiveness in classifying all acquired gestures. The performance of the proposed model is evaluated against other DL‐based methodologies commonly employed in surgical gesture classification. The results indicate that the proposed approach outperforms these benchmark methods, achieving higher classification accuracy and robustness in distinguishing diverse surgical gestures.