## 6 Discussion and Conclusions  
The present study investigates the use of machine-learning (ML)-based surrogate models for vibroacoustic analyses. We show how to tackle the lack of interpretability of black-box simulators and how to determine the surrogates' capacities to fit the non-smooth functions which are recurrent in the vibroacoustic domain. As a study case, surrogate models were constructed for sound transmission loss (STL) analyses modeled at different complexities levels, including analytical and numerical approaches. The physical consistency of the surrogate models was verified through sensitivity analyses intrinsic to the ML methods, without additional computational cost. For each region of  
Figure 16: Range of the input variables used for each design space considered (**a**–**c**), the volume of the design spaces relative to the volume of the standard design space \(\mathcal{D}\) (**d**) and the range of critical frequencies resulting from each design space (**e**): (**a**) thickness; (**b**) density; (**c**) young modulus; (**d**) design space volume; (**e**) critical frequency. Figure 17: NN-based surrogate accuracy for the design spaces \(\mathcal{D}\), \(\mathcal{D}^{-}\), \(\mathcal{D}_{1}^{+}\) and \(\mathcal{D}_{2}^{+}\) when modeling the STL problem with different approaches: (**a**) infinite plate; (**b**) correction factor; (**c**) modal summation; (**d**) modal summation with \(1/3\) octave band average. the frequency spectrum, the physical behavior identified by the features' importance results were in accordance with the STL theory. Moreover, aspects such as the differences between the STL models were inferred from the sensitivity study, providing a deeper understanding of the modeled phenomena. The benchmarking of surrogates based on four ML methods, namely neural networks (NN), Gaussian process regressor (GPR), random forest (RF) and gradient boosted trees (GBT) show that NN consistently performs better. The surrogate presented satisfactory accuracy even for functions with highly non-smooth behavior resulting from resonant and coincidence phenomena. Furthermore, it is shown that including domain knowledge through physics-guided features improves the surrogate performance for all ML methods and STL models. The surrogate errors are also shown to be proportional to the design space size for the surrogate with less complex STL models but do not change significantly with the design space size for the STL with high non-smooth responses. On the other hand, the location of the design space in the input domain has a relevant impact on the accuracy in all cases. Although the results were generated for the case of STL, some conclusions can be generalized to guide the implementation of accurate surrogates for other vibroacoustic problems with similar behavior. First, sensitivity analysis methods and the inclusion of physics-guided features can be readily applied to other physical domains. Second, the capability of the ML-based surrogate, especially the NN-driven, to predict non-smooth behavior was observed in the case of STL and is an indicator for other vibroacoustic analyses. Therefore, this paper presents good practices and methods to create ML-based surrogate models for vibroacoustic problems with improved interpretability, accurac, and physical guidance, increasing confidence in the model. The vibroacoustic surrogates obtained with those practices can be used as an informed and fast decision-making tool, which is well-suited for real-time applications, the construction of digital twins and robust and optimal product design where extensive domain exploration is required. Furthermore, this work may be extended to include physical constraints in the surrogate to guarantee the model's physical consistency. Conceptualization, B.Z.C., A.-M.Z., M.I., C.D. and S.F. ; methodology, B.Z.C. ; software, B.Z.C. ; validation, A.-M.Z., M.I. and C.D. ; formal analysis, B.Z.C. ; investigation, B.Z.C. ; resources, M.I. and S.F. ; writing--original draft preparation, B.Z.C.