## 2 Numerical Modelling  
To investigate the thermal response of reinforced concrete under microwave excitation, we employed a two-stage approach combining numerical simulation with experimental verification. The first stage focuses on computational modeling, where we developed a simulation environment capturing key aspects of the physical setup. The central aim of the numerical modeling performed in this study was to generate a set of synthetic thermal images to be used for training a convolutional neural network (ResNet-18) tasked with detecting the position of reinforcement bars within concrete structures. The thermograms were not intended as isolated simulations for analytical evaluation but rather as a curated dataset reflecting controlled physical conditions under which specific surface thermal signatures emerge due to microwave excitation. The simulated system included a broadband aluminum horn antenna as the microwave radiation source and a reinforced concrete slab containing eight parallel steel rebars. The layout of the reinforcement bars remained constant throughout all simulations: the bars had a diameter of 12 mm, were arranged with 100 mm spacing, and were embedded in a concrete block measuring 800 mm \(\times\) 800 mm \(\times\) 65 mm, with a 15 mm cover layer above the rebar on the side facing the antenna. These particular elements of the setup are presented in Figure 2.  
The variations introduced in the simulations are related to external measurement conditions and geometry. Specifically, two modes of microwave excitation were considered:  
* Continuous mode, in which power was supplied at a constant rate over a fixed duration;
* Modulated mode, where the input power followed a predefined periodic function. In the modulated mode, the power input was governed by a cyclical pattern, as depicted in Figure 3. The modulation protocol implemented a 30 s repeating cycle, consisting of 23 s of sustained maximum power delivery, followed by a 7 s interval during which no power was applied. Figure 2: Geometric components used in the numerical model: (**a**) broadband horn antenna; (**b**) concrete specimen with embedded steel reinforcement bars. Additionally, the orientation of the specimen with respect to the antenna was systematically varied. Different angles of inclination were modeled to analyze how the spatial relationship between the antenna and sample affects the microwave energy distribution, and consequently, the resulting thermal pattern on the surface. Precisely speaking, the angle between the sample and the antenna was parameterized in the conducted simulation, taking on four values: 0, 15, 30, and 45 degrees, as illustrated in Figure 4.  
Simulations were carried out using COMSOL Multiphysics 6.3, which allowed us to couple electromagnetic wave propagation with transient heat transfer in a unified finite element framework. Of particular importance was the thermal behavior of the concrete immediately above the reinforcement bars. While microwaves do not significantly penetrate or directly heat the steel (due to its extremely low skin depth), the steel acts as a thermal and electromagnetic disturbance. It impedes heat dissipation into the bulk material and causes localized heating of the concrete layer above. Moreover, due to the conductive nature of the steel, electromagnetic wave interference and diffraction were observed, further influencing the surface temperature distribution. The geometry of the proposed numerical model is depicted in Figure 5.  
Figure 4: Four numerical simulation scenarios: (**a**) sample positioned directly in front of the antenna (\(0^{\circ}\)), (**b**) sample inclined at \(15^{\circ}\), (**c**) sample inclined at \(30^{\circ}\), and (**d**) sample inclined at \(45^{\circ}\). Figure 3: Time-dependent modulation signal applied as a heating excitation in numerical modelling.