###### Abstract
An alternate approach lies in the idea of decoupling the time and space domains of the underlying differential equations. This approach, named Proper Generalized Decomposition (PGD), is known to avoid the curse of dimensionality [48]. Using this scheme, a global-local model for beams is presented by [PERSON] et al. [49], who model the main parts of the beams using the wave finite element method, while the section around the defect is modeled via conventional finite element method (FEM). Another surrogate, which relies on the combination of Bayesian optimization with a machine learning approach, enables uncertainty quantification with respect to the material parameters in composite plates [50]. Furthermore, in the framework of SHM, [PERSON] et al. [51] created a metamodel with radial basis functions. As this metamodel can rapidly evaluate the response for different defect locations, it can be combined with PSO to localize damage in a single-defect scenario. Surrogate models based on ray tracing track individual wave packets through the plate, allowing for gathering further information about the wave packets at the sensor location. The sensor response is then found by summing the single wave packets together. Furthermore, the computational time of such surrogates is independent of the size of the plate. Ray tracing can be performed using the pencil method, where the wave is tracked with an axial ray and a paraxial ray is introduced to track its amplitude [52]. The method is able to model reflections and mode conversion precisely, even at curved edges and allows for modeling wave sources of finite size. This method was extended to model laminate plates [53]. [PERSON] et al. [54] combined the pencil method with the wave finite element method to model wave propagation in plates with joints. In this concept, the wave finite element method models the transition at the joints, while the pencil method tracks the energy of the wave. Based on an analytical scattering model, [PERSON] et al. [55] provide a ROM that uses a dictionary approach for the scattering, which is combined with the modeling of edge reflections through mirroring. Localizing a single defect with this model outperforms the DAS method regarding the necessary receivers to accurately localize the defect. Similarly to this approach, we explore a surrogate with ray tracing, relying on a numerical model to create a dictionary for the scattering behavior. [PERSON] et al. [56] modeled the scatterer with finite elements and the area of the pristine plate through semi-analytical solutions for half-spaces. The decoupling of the space around a defect (near field) and the far field is also the base of the model introduced by [PERSON] et al. [57]. They modeled both fields with different versions of the Scaled Boundary Finite Element Method (SBFEM) and coupled the models with the mortar method. Another analytical scattering model was introduced by [PERSON] et al. [58], who explored a damage index based on the amplitude of the scattering model for an estimation of the damage size. A fast analytical predictor is also given by [PERSON] and [PERSON] [59], who split the area around notches and cracks in several different domains and adjust the boundaries of the domains according to the neighboring domains. This model is called Complex Modes Expansion with vector Projection (CMEP). Generally, as seen in the aforementioned ray tracing models, the scattering behavior of defects and flaws needs to be investigated carefully, as it significantly influences the sensor response. Such investigations have been performed numerically [60; 61; 62; 63; 64], analytically [61; 64] and experimentally [62; 63; 64] for different types of defects. The results of these analyses indicate that the reflection is dependent on the mode and frequency of the incident wave [63]. [PERSON] et al. [61] derived an analytical formulation for the scattering of the \(S_{0}\) wave mode by coupling the Poisson plate theory with the Mindlin plate theory.