## 1 Introduction
However, in the same work it can be noted how the estimation of peculiar acoustic performance indicators of meta-materials, such as the percent increase of absorption coefficient or Transmission Loss (TL) peak when passing from a homogeneous medium to a material with embedded inclusions, lacks analytical formulation, therefore pushing towards the use of numerical simulations or experimental tests, with all that derives in terms of financial expenses, computational time, experimental setup, etc. For these reasons, it is reasonable to investigate alternative techniques, such as machine learning methods, which may be able to provide automated and quick estimations of the acoustic performances of meta-material packages, which may be useful in preliminary design phases or more advanced characterization tasks. Potentially, this may lead to noticeable money and time savings. In particular, machine learning is a subset of Artificial Intelligence (AI) in which several disciplines, such as computational statistics, pattern recognition, image processing, data mining, adaptive algorithms, etc., converge. Machine learning methods allow a computational device to perform predictions in an automatic way by learning from a set of data and exploiting the information underneath, by improving the performances on a specific task from data without being explicitly programmed. A formal and more enlightening definition is given by [PERSON] [30], which states that: \"A computer program is said to learn from experience \(E\) with respect to some class of tasks \(T\) and performance measure \(P\), if its performance at tasks in \(T\), as measured by \(P\), improves with experience \(E\)\". The fact that there is not a task-specific algorithm, confers a high versatility to the approach, which allows its application in several research fields. Thus, it is not surprising that recently, machine learning methods have received increasing attention dedicated to the analysis of the transmission and dispersion properties of periodic acoustic meta-materials, characterized by the presence of local resonators. [PERSON] et al. [31] and [PERSON] et al. [32] provide interesting reviews on machine learning applied to acoustics. Novel functional applications in the optimal parametric design of smart tunable mechanical filters and directional waveguides involving the use of machine learning techniques are proposed by [PERSON] et al. [33], as well as [PERSON] et al. [34], who use adversarial neural networks for the design of acoustic meta-materials, while the same topic is addressed, with cloaking as ultimate goal, by [PERSON] et al. [35] through reinforcement learning. Both genetic algorithms and neural networks models are adopted in the literature [36], representing an effective approach in order to design acoustic meta-materials. In particular, as an efficient machine learning method, deep learning has been widely used for data classification and regression in recent years, showing good generalization performance [37]. [PERSON] and [PERSON] [38] train artificial neural networks with sound absorption coefficient measurements. Material properties are investigated by [PERSON] et al. [39], which reverse-engineer sound absorbing materials in order to obtain features from the absorption coefficient. In the present work, the effectiveness of machine learning methods as tools for performing the characterization is evaluated, in terms of TL peak frequency and percent increase (with respect to the homogeneous configuration) of meta-material acoustic packages in which the porous phase is described with two different models, namely, Delany-Bazley-Miki (DBM) and Johnson-Champoux-Allard (JCA) models. In particular, the proposed acoustic package is made of an arrangement of periodic porous unit cells with perfectly rigid inclusions.