Performance evaluation of BEM and PINNs

(Top) Relative error versus solution time for BEM with varying numbers of integration points and for PINNs with different network architectures. Shaded horizontal bands indicate the ranges between the minimum and maximum times for each method. Labels at the right of the plot identify the three groups: PINN (training), BEM (solution), and PINN (evaluation). The green highlighted points correspond to the selected configurations, (𝐿 = 3, 𝑁 = 75) for the PINN and 𝑛 = 15 for the BEM, which were used for the direct comparison of computational times, where 𝐿 is the number of hidden layers, 𝑁 the number of neurons per layer, and 𝑛 the number of integration points. (Bottom) Spatial distributions of the relative error in amplitude and phase are shown for the selected BEM and PINN configurations.