## 1 Introduction  
The Fundamental Period (FUP) of buildings is a very important parameter in the context of new structures' seismic design. Moreover, it is a crucial feature that can be used to determine existing buildings' seismic capacity [1, 2]. The design spectrum of available seismic codes in combination with the estimated FUP can lead to the determination of the forces introduced by a seismic excitation in a building, i.e., the calculation of the seismic base shear. Furthermore, the FUP is a crucial feature that can be employed under the corresponding acceleration spectrum for near-real-time estimation of the seismic forces introduced on buildings by a strong seismic excitation. In this way, the level of seismic damage can be macroscopically estimated and documented [3, 4]. However, as is well known, calculation of the fundamental period requires the solution of an eigenvalue problem. The formulation and solution of this problem under the finite elements' framework requires knowledge of the values of numerous parameters to be used in estimating the stiffness and mass matrix of the building [5, 6]. Furthermore, in the design of new buildings, the values of the above parameters cannot be known before the final design. Therefore, it is particularly useful to develop approximation methods for estimating FUP. This can be achieved by considering only some of the problem's parameters that can be easily calculated at the design stage of new buildings, or by directly estimating them by working on already existing buildings, e.g., buildings for which a rapid assessment of their seismic capacity has been performed before or after a strong seismic excitation. In particular, for the case of new reinforced concrete (RC) buildings, in recent decades the respective design codes [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18] have globally incorporated approximate equations for the estimation of FUP, recognizing its usefulness in the design process. However, in addition to these codes, the formulation of approximate equations for the calculation of the fundamental period has been the subject of a significant number of research papers [19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. These research studies have utilized instrumental measurements of buildings during strong seismic excitations as well as measurements of ambient vibrations. In addition, numerical finite element models have been used to increase the number of buildings from which the FUP equations have been developed. The obtained results have been used both to document the existing approximate equations of the codes and to improve them. One of the parameters that can significantly affect the value of the fundamental period is the masonry infill. Through a series of numerical and experimental researches, it has been shown that masonry infills can significantly increase the horizontal stiffness of RC buildings, resulting in a significant change in the seismic forces that they receive. Thus, specific study to assess the influence of masonry infills on the FUP approximation equations has been the subject of a significant number of research papers [34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44]. Statistical processing of instrumental measurements or results obtained from computational analyses is a basic research approach aiming at the formulation of approximate equations for the estimation of FUP in RC buildings. This can be done with or without masonry infills. In this approach, the problem is reduced to the processing of available databases containing values of the fundamental periods of buildings with different structural characteristics. In this regard, the recent rapid increase in the use of machine learning (ML) algorithms for solving civil engineering problems [45; 46; 47; 48; 49] has provided a new perspective on the investigation of equations for estimating the fundamental periods of RC buildings with masonry infills (RCB_MI).