## 3 Method
### Algorithmic Implementation
The method can be extended to account for further intricacies, including geometries that accommodate diversified plate setups. The authors expect that an extension to anisotropic plates is possible with more training simulations. 3. The full time history at the sensor location is reconstructed, and not only the arrival time or the amplitude, as furnished by commonly adopted alternatives. 4. The mechanics behind the surrogate is well understood. Rooting the method in mechanics principles reduces the training effort, with only few simulations required for training, while ensuring that the model estimates can be extrapolated. Furthermore, the process allows for tracking single wave packets through various possible propagation paths, which allows gaining information on the individual wave packets present in the sensor response. This allows a better understanding of the wave propagation phenomena, which is superior compared to the classical FOMs. Building on the proposed method, several promising avenues for further research can be explored. While the current approach focuses on circular defects, a modified training strategy could enable its application to more complex geometries, significantly expanding its versatility. To further enhance efficiency, investigating the relationship between scattering wave characteristics and defect size could reduce the need for extensive training simulations. Notably, [PERSON] et al. [64] observed that for holes, the amplitude of scattering waves is nearly proportional to their diameter--an insight that could be leveraged to refine the model. For real-world applications, incorporating boundary reflections is essential. A key step in this direction is analyzing the interaction between different wave modes at the boundary, such as shear horizontal and anti-symmetric modes [52]. Additionally, extending the method to anisotropic materials presents an exciting opportunity to account for direction-dependent wave propagation speeds, further broadening its applicability. Optimizing sensor placement also holds great potential. While the current offline approach employs a regular grid, a strategically optimized placement could minimize errors, as observed in Figure 14b. Finally, enhancing computational efficiency through parallelization and adaptive stopping strategies would further accelerate the surrogate model, making it even more effective for practical use. Conceptualization, P.S., E.C. and K.A. ; methodology, P.S., E.C. and K.A. ; software, P.S. ; validation, P.S. and K.A. ; formal analysis, P.S. ; investigation, P.S. ; writing--original draft preparation, P.S., E.C. and K.A. ; writing--review and editing, P.S., R.S., W.O., E.C. and K.A. ; visualization, P.S. ; supervision, E.C. and K.A. ; project administration, E.C. ; funding acquisition, W.O. and E.C. All authors have read and agreed to the published version of the manuscript. This research is conducted as part of the project \"Fusion of Models and Data for Enriched Evaluation of Structural Health\" financed by the National Science Center (Poland) and the Swiss National Science Foundation (200021L_192139). The authors also wish to acknowledge the MSCA Staff Exchanges 2021 project ReCharged (Grant ID: 101086413). This project has received funding 505 from the Horizon Europe Programme under the Marie Sklodowska-Curie Staff Exchanges Action (GA no. 101086413), co-funded by the UK Research & Innovation and the Swiss State Secretariat for Education, Research & Innovation. Dr [PERSON] acknowledges the support of the COST Action HISTRATE CA21155. Not applicable. No new data were created or analyzed in this study. Data sharing is not applicable to this article. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: