## 1 Introduction  
Concrete structures are subjected to repeated loading (\(N\)) from many sources, such as dead load and live loads in buildings, traffic loads in civil structures, or environmental loads, such as temperature and humidity changes. It is commonly known that concrete strength under repeated loading will be lower than that under static loading [1, 2]. Concrete structures subjected to many repeated loadings will experience an increase in deflections, crack widths, and eventually lead to the reduction in durability and fatigue failure [3]. A classic fatigue equation for plain concrete is typically represented by an \(S\)-\(N\) diagram, where the stress level (\(S\)) is defined as the percentage of the static strength, with respect to the logarithm of \(N\). Most previous research results on fatigue have been analyzed with a simple linear equation. However, it is well-known that the single \(S\)-\(N\) curve (known as a Wohler curve) is inappropriate to describe fatigue behavior [1], as it is affected by other factors. In addition to \(S\), concrete fatigue is affected by various factors, such as concrete compressive strength, concrete mix proportions, and loading parameters [1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]. As stated in [1], unlike insensitivity to the details of mix design and concrete compressive strength, concrete is highly sensitive to fatigue loading parameters, such as maximum stress level (\(S_{\text{max}}\)), maximum stress to minimum stress level (\(R\)), frequency (\(f\)), and fatigue loading history [1]. Moreover, high strength concrete yields a different fatigue pattern, while various mix designs proportioned by different water-binder ratios, including the use of fibers, also produce different fatigue patterns [1]. Recently, incorporating supplementary cementitious materials (SCMs), such as slag, fly ash, metakaolin, and silica fume, in the concrete mix is widely regarded as the most economical means of improving durability and reducing CO\({}_{2}\) emission issues [34; 35]. Thus, in the near future, it will be essential to understand the fatigue behavior of the waste materials, as well as the SCMs. However, the fatigue behavior of innovative concrete materials combined with the above-mentioned mixture constituents is difficult to estimate. In addition, the concrete structures will be exposed to diverse fatigue loading parameters, such as different stress levels and frequencies, as mentioned before. Therefore, the traditional statistical treatment of accurately predicting concrete fatigue behavior has reached its limit, due to its inability to consider the complicated combined effects of those influential parameters. To overcome this limitation inherent in the traditional regression-based statistics methods, a machine learning (ML) method has been introduced to solve complex concrete material properties in terms of durability, as well as mechanical strengths [4; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. In recent years, the ML method has become more widely used for structural and material design in civil engineering. Various ML methods have been frequently used since 2020 for predicting basic mechanical strength properties [36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61] and mixture optimizations [36; 39; 62]. The main concrete property that has been predicted using the ML method is the compressive strength of various concretes, such as normal concrete [36; 37; 38; 39; 40; 41], high performance concrete (HPC) [38; 42; 43; 44], concrete with industrial wastes, including supplementary cementitious materials (SCMs) [45; 46; 47; 48; 49; 50; 51; 52; 53; 54], recycled aggregate (RA) concrete [52; 55; 56; 57], geopolymer concrete [58; 59], and concrete with fibers [53].