## 2 Physics-Driven Models of Sound Transmission Loss  
When an acoustic wave hits a plate, it is partially reflected in the incident acoustic field and partially absorbed by the plate itself. Most of the absorbed portion excites the plate,making it vibrate and radiate noise in both the incident and transmitted fields, as illustrated in Figure 1. The STL is defined by the ratio between the incident sound power \(P_{I}\) and the sound power transmitted through the plate \(P_{T}\), being usually evaluated in decibels as  
\[STL=10\log_{10}\left|\frac{P_{I}}{P_{T}}\right|^{2}. \tag{1}\]  
The transmitted noise is inversely proportional to the system effective impedance, which is the sum of the mechanical impedance of the plate and the fluid-loading impedance [24]. The effective impedance depends on the fluid properties, the incident \(\theta\) and azimuth \(\phi\) angles of the incident wave and the material, dimensions, and boundary conditions of the plate. This paper considers that the incident field is a random field of incident plane waves in all directions, known as a diffuse field. At frequencies below the first natural frequency of the plate, the plate dynamics influence on the STL is negligible, and the STL is controlled by the plate bending stiffness,  
\[D=\frac{Eh^{3}}{12(1-\
u^{2})}(1+i\eta), \tag{2}\]  
where \(h\) is the thickness, \(E\) is the elastic modulus, \(\
u\) is the Poisson's ratio, and \(\eta\) is the damping loss factor of the plate. When the driving frequency is close to the first natural frequencies of the plate, the resonant behavior of the plate governs the STL. As the frequency increases and the resonant behavior attenuates, the plate behavior approaches that of a lim mass, especially for thin plates in frequencies where the bending stiffness is not relevant. At this frequency range, the STL depends solely on the surface mass density \(m=h\rho\) and can be approximated by the mass law, as demonstrated in [24]. With the increase in frequency, the coincidence phenomenon takes place, and the mass law is no longer valid. The coincidence happens when the trace velocity of the acoustic wave projected in the plate is equal to the velocity of its natural bending wave. These waves superpose and create a scenario of minimal impedance, maximizing the transmission of sound. The coincidence frequency \(\omega_{coinc}\) in which the trace and the bending wavenumbers coincide is evaluated by:  
\[\omega_{coinc}=\frac{c_{0}^{2}}{\sin^{2}\theta}\sqrt{\frac{\rho h}{D}}, \tag{3}\]  
where \(c_{0}\) is the characteristic sound speed, and \(\rho\) is the plate density. The minimum frequency in which coincidence occurs is for grazing incidence (\(\theta=90^{\circ}\)) and is called critical frequency \(\omega_{crit}\), where the amplitude of the valley in the STL is controlled by the plate damping. Above the critical frequency, the coincidence phenomenon occurs for gradually smaller incidence angles, and the STL is controlled by the plate bending behavior. Figure 2 illustrates a typical STL curve and its influence regions. Figure 1: Illustration of the sound transmission loss (STL) analysis of a plate. In the literature, different STL models capture the aforementioned curve behaviors with distinct levels of detail [23]. In this paper, four STL methodologies described in Section 2.1 are implemented to evaluate the ML-based surrogate capabilities. The first and simplest methodology considered is the analytical STL solution for an infinite plate. As the unbounded infinite plate is not affected by the resonances, the STL in low frequencies relies only on the surface density mass. To account for the plate width \(a\) and length \(b\), the radiation efficiency of a finite plate may be considered instead of the radiation efficiency of the infinite plate.