## 3 Method
### Algorithmic Implementation
Finally, the results for the case where Feature 1 corresponds to a hole and Feature 2 is a notch can be seen in Figure 18, where, again, the main wave packets are captured in amplitude and phase. The additional sensor locations marked in

Figure 8.1 Response at the sensor location (0.09! 0.09) for the case where Feature 1 is a notch and Feature 2 is inactive. (**a**) Symmetric excitation (error = 0.0264). (**b**) Anti-symmetric excitation (error = 0.0258). Figure 8.2 Response at the sensor location (0.05! -0.04) for the case where Feature 1 is a notch and Feature 2 is inactive. (**a**) Symmetric excitation (error = 0.0081). (**b**) Anti-symmetric excitation (error = 0.0289). Figure 12, including those within the defect region, showed similar accuracy to the results presented in the presented plots. ### Speedup

All surrogate simulations were performed on a single Intel(R) Xeon(R) Gold 5318Y CPU @ 2.10 GHz core using Matlab 2024a [94], while the FOM simulations were run on the ETH Euler cluster with eight core AMD EPYC 7742 processors (2.25 GHz nominal, peak of 3.4 GHz). The surrogate simulations with a single feature take approximately 0.5 s and with two features approximately 4.4 s for the seven sensors displayed in Figure 8.3 On the other hand, the computational time for the FOM is nearly independent of the features, corresponding to 1.6 h for each simulation. For the cases considered and when using the described hardware, this results in a speedup in the order of \(10^{3}\) to \(10^{4}\). In addition, tests including three and four features were performed, where the simulations were run for approximately 16 s and 49 s, respectively, resulting in a speedup in the order of \(10^{2}\). Generally, the computational time for the surrogate depends heavily on the number of features that are assumed to be present, but only indirectly depends on the size of the plate

Figure 8.4 Response at the sensor location (0.05 \(-\)0.04) for the case where Feature 1 is a hole and Feature 2 is a hole. (**a**) Symmetric excitation (error = 0.0207). (**b**) Anti-symmetric excitation (error = 0.0367). Figure 8.5 Response at the sensor location (0.05 \(-\)0.04) for the case where Feature 1 is a hole and Feature 2 is a notch. (**a**) Symmetric excitation (error = 0.0136). (**b**) Anti-symmetric excitation (error = 0.0311). (through the attenuation and the propagation time). Conversely, computing the FOM is heavily dependent on the size of the plate, while the effect of the features on the numerical toll is only minor, albeit implying a required mesh modification. ## 5 Discussion

We introduce an approach to efficiently model guided wave-based sensing scenarios by delivering a surrogate for rapid evaluation of Lamb wave propagation. The method can flexibly account for diverse geometrical features and is easily extendable to more complex setups. In this study, which serves more as an introduction to the approach, we place the following specific assumptions:

1. The plate is assumed to be composed of a linear-elastic and isotropic material. 2. The area where the excitation is applied, the features, and the sensors are considered small compared to their interconnecting distance and can, therefore, be assumed to be point-wise. 3. The explored frequency range is chosen so that only fundamental modes are propagating and only the out-of-plane displacement is investigated. 4. No viscous damping is assumed. Most of these assumptions can be relaxed, while others are allowed for the usual cases explored within the Non-Destructive Evaluation (NDE) and SHM contexts, given the small amplitude of actuated Lamb waves. The method introduces a new approach to modeling GW-based assessment, featuring the following advantages:

1. The computational cost of the surrogate is significantly lower to the FOMs and therefore suited for inverse problem settings, as mandated in condition monitoring and damage diagnosis tasks. In the provided examples, the speedup is in the order of \(10^{3}\) to \(10^{4}\). 2.