## 8 Concluding Remarks  
This work extends previous research on the development of surrogate models for the aerodynamic and aeroelastic characterization of long span bridges. The fundamental challenge addressed herein has been the multidimensionality in the inputs of the surrogate model, as four input design variables were considered for the definition of the force coefficients surrogate model: the width and depth of the individual boxes, the gap distance between boxes and the angle of attack. Similarly, for the flutter derivatives surrogate model, the input variables adopted were the width and depth of the individual boxes, the gap distance between boxes and the reduced velocity. Another challenge has been the computation of the flutter derivatives for the 15 samples considered in the definition of the surrogate by means of 2D URANS forced-oscillation simulations in the pitch and heave degrees of freedom at five different reduced velocities. This more burdensome approach was required, as the consideration of large gap distances in the twin-box deck arrangements does not allow for the application of the quasi-steady theory for the approximation of the flutter derivatives adopted in other cases by the authors. In addition to the implicit computational burden, spatial and temporal verification studies have been completed, and the numerical data have been validated with the experimental data for a subset of three geometries within the set of samples resulting from the application of the LHS method. The surrogate model of the force coefficients enables the identification of larger sensitivity in the lift and moment coefficient with the box width and depth, while the gap-to-depth ratio plays a decisive role only in the lift coefficient. For the flutter derivatives, the surrogate model shows a strong dependence in the values with the gap-to-depth ratio for any given reduced velocity for \(H_{1}^{*}\), \(H_{2}^{*}\), \(A_{1}^{*}\) and \(A_{2}^{*}\) but a minor influence for \(H_{3}^{*}\) and \(A_{3}^{*}\). This last flutter derivative is, however, more affected by changes in the box width \(C\). Furthermore, it is also interesting to note how, for a given flutter derivative and gap to depth ratio \(G/D_{\text{ref}}\), the qualitative influence of the deck depth \(D\) and box width \(C\) is also dependent on the reduced velocity. For instance, flutter derivatives \(H_{1}^{*}\) and \(H_{3}^{*}\) show different trends with \(C/C_{\text{ref}}\) and \(D/D_{\text{ref}}\), as the reduced velocity increases for a given gap distance. On the other hand, flutter derivatives such as \(H_{2}^{*}\) and \(A_{2}^{*}\) show similar patterns with \(C/C_{\text{ref}}\) and \(D/D_{\text{ref}}\), independently of the reduced velocity for a given \(G/D_{\text{ref}}\) ratio. The impact of the changes in the twin-box deck geometry in the flutter response has been analysed based on the stabilizing or destabilization effect, depending on the values of each individual flutter derivative, following [38]. In addition to the qualitative and quantitative interpretation of the aerodynamic and aeroelastic parameters, the surrogate model is ready to be applied in the application of surrogate-based design optimization problems considering the flutter, buffeting and aerostatic stability, following the methodology outlined in [2]. As surrogate modelling techniques gain maturity, further advances would improve our understanding of the aeroelastic responses of long-span bridges. In this regard, adding additional geometric input variables, such as the length and angle of a recessed lower internal corner or the fairing corner angle, would enable a more precise tailoring of the desired flutter response, although at the expense of higher dimensionality in the model and, therefore, larger computational demands.