## 1 Introduction
In a subsequent step, a Kriging surrogate model was defined for the force coefficients and their slopes at a \(0^{\circ}\) angle of attack, enabling the approximation of the flutter derivatives, adopting the quasi-steady theory. Finally, the surface response for the critical flutter speed over the considered design domain was obtained for two application cases. In [23], the previous framework was extended by including an additional design variable: the gap distance between girders. In that case, the definition of the samples over the three-dimensional design domain (box width, box depth and gap distance) was carried out by applying the random Latin Hypercube Sampling (LHS) method. Afterwards, a Kriging surrogate model was trained using the aerodynamic outputs obtained for 25 samples evaluated using a 2D URANS approach. In the application case, the gap to depth ratio range considered was \(G/H=(0.51,1.86)\) inside region 1, as defined in [24]. Given the relatively short gap-width considered, the flutter derivatives were successfully approximated by the quasi-steady formulation, requiring a correction in the values of the aerodynamic centres. The present research effort extends the research on this subject by addressing the following limitations in previous studies: (i) In addition to modifications in the width and depth of the individual boxes of the twin-box deck, large gap-widths inside region 2 [24] were considered herein, in order to cover a more general design problem. Targeting large gaps in surrogate-based design is relevant, as experimental parametric studies have considered gap widths inside region 2, and, for instance, the Stonecutters Bridge features a gap to depth ratio of 3.7. (ii) The consideration of large slots between girders has required dropping the quasi-steady assumption for the approximation of the flutter derivatives adopted in previous research. Consequently, forced-oscillation simulations were implemented for the numerical evaluation of the flutter derivatives for the considered set of samples defining the surrogate model. In fact, this approach yields a multidimensional surrogate model for the approximation of the flutter derivatives at \(0^{\circ}\) angle of attack (AoA), which comprises the following four (4) input variables: box width, box depth and gap distance in the twin-box deck, along with reduced velocity. (iii) Furthermore, the computational burden associated with the forced-oscillation simulations at different reduced velocities for the heave and pitch degrees of freedom is substantially higher than that associated with the evaluation of the force coefficients at a given angle of attack. To the authors' knowledge, forced-oscillation simulations have previously never been adopted in surrogate modelling training. (iv) Finally, the nonlinearity of the aeroelastic response following changes in the deck geometry of twin-box decks has been highlighted by other researchers without outlining the global patterns; therefore, a surrogate model based on the Radial Basis Function (RBF) has been developed herein in order to identify and shed some light on the general trends in the aeroelastic response. It is important to note that twin-box decks are prone to vortex-induced vibration (VIV), which is a phenomenon highly dependent on the gap distance between girders [24; 25; 26; 27; 28]. The remainder of the article is organized as follows: A brief review of the fundamental formulation is provided, addressing force coefficients, flutter derivatives, Navier-Stokes equations and the Radial Basis Function (RBF) formulation for the definition of the surrogate model. In the next section, the application case is introduced, and the design of experiments methodology based upon the Latin Hypercube Sampling (LHS) method is reviewed.