## 2 Materials and Methods
### Design of Generic Porous Media Samples  
Within this contribution, generic porous media are investigated that are designed using a simple bar-lattice design. The general design is shown in Figure 1a. The specimen have a circular shape with a diameter of 30 mm. The specimen thickness \(l\) is 15 mm. These quantities are kept constant within this contribution. The inner geometry is determined by a certain number of layers stacked upon each other, each layer consisting of a lattice of parallel bars. The geometry of each bar is determined by the bar width \(d\) and the bar height \(h\). The bars of each layer are spaced by the bar spacing \(s\). Moreover, from one layer to the next (direction bottom-up), each bar lattice is turned by the plane angle \(\varphi\). The variables \(d,h,s,\varphi\) are hereafter referred to as design variables, since they fully determine the microscale geometry of the specimen. A photograph of one sample is shown in Figure 1b. The specimens are produced using additive manufacturing (also known as 3D-printing). A more detailed description on the manufacturing of the specimen can be found in [36]. In order to allow for a machine-learning-based modeling of the relation between the specimen microscale and the resulting porous media model parameters, a Latin  
Figure 1: Photograph and schematic design of the generic porous media samples. (**a**) Design variables used to parameterize the material properties [36]. (**b**) Photograph of a printed generic porous media sample [36]. Hypercube Sampling (LHS) of the design variables is conducted using the parameter ranges given in Table 1.  
Based on the LHS-procedure and the parameter ranges given in Table 1, a set of 50 specimens is produced. These fill the parameter space, and thus exhibit various acoustic properties. In order to generate the input data required for the inverse parameter identification described in Section 2.2, the parameters flow resistivity \(\Xi\) and absorption coefficient \(\alpha\) of all specimens are measured. The flow resistivity is measured using the alternating flow method based on ISO 9053-2 [50], and the absorption coefficient is measured using the two-microphone technique in an impedance tube based on ISO 10543-2 [51] in the frequency range of 900-6600 Hz. For more details on the measurement, the reader is asked to refer to our preceding contribution [36]. Figure 2 shows the measured flow resistivity (Figure 2a) and the measured absorption coefficient (Figure 2b) of all specimen. In Figure 2, the measurement results of all specimens are shown in gray color, while two are colored separately. The sample with the highest mean absorption coefficient is marked in orange (specimen no. 2, counting 0-49); the sample with the lowest mean absorption coefficient (specimen no. 39) is marked in blue. These samples are seen as somewhat extreme samples regarding the absorption coefficient. However, it can be verified from the results of the flow resistivity that these specimens do not show extreme values for this quantity. Thus, the flow resistivity cannot serve as the only explanatory variable for the general behavior of the material with regard to the absorption coefficient. This finding motivates the approach to model the relation between the model parameters and the microscale geometry using machine-learning. It is expected that a machine-learning model--here, specifically, a neural network--can model the (expected) nonlinear relationship between the microscale geometry and the acoustic model parameters and can be trained based on the available experimental data. Therefore, an inverse parameter identification procedure is pursued to extract the acoustic model parameters based on the measured quantities flow resistivity and absorption coefficient. This is described in the following section.