## 1 Introduction  
Recently, artificial intelligence (AI) and artificial neural network (ANN) models have been widely utilized to solve engineering problems [1; 2]. Machine learning approaches have emerged as powerful tools for addressing nonlinear problems and gaining valuable insights from complex systems [3; 4]. These approaches harness the computational capabilities of artificial neural networks, such as multilayer perceptron architectures, to capture and analyze the nonlinear dynamics inherent in these systems. By training neural networks on data obtained from complex systems, researchers have successfully captured their underlying behaviors, enabling precise predictions and enhanced control of these systems [5]. In particular, ANNs have been used to ease the design and improve the performance of electronics devices, such as microwave devices [6; 7; 8]. Filters and power dividers are vital blocks in new microwave and communications circuits [9]. In modern microwave circuits, a compact size and harmonics rejection are required to reduce the circuit area and costs [10]. Additionally, rejection of harmonics results in the improvement of the the given system's overall performance [11]. The conventional power dividers previously used in microwave circuits occupy a large area, and cannot reject undesirable harmonics. Therefore, recently, different designs have been introduced to overcome these drawbacks. Previous research aiming to counteract the disadvantages of conventional power dividers are explained in the following section. Nonlinear phenomena present significant challenges when it comes to comprehending and predicting the behavior of complex systems. This holds true in various engineering fields, including microwave circuit design, medical engineering, industrial engineering, etc., wherein accurate modeling and analysis play a vital role in optimizing performance and ensuring reliability [12; 13; 14; 15]. However, traditional analytical approaches often struggle to capture the intricate dynamics exhibited by nonlinear systems, prompting the exploration of alternative methods [16]. EBG and DGS techniques have been used in [17; 18; 19] to decrease the circuit size and suppress undesirable harmonics. However, these methods require extra steps in the device implementation process, which is undesirable. In some works [20; 21; 22], open stubs have been used for harmonics suppression and size reduction purposes. However, only a few harmonics can be suppressed using open stubs, and a significant reduction in size cannot be obtained. A WPD with two main open stubs and three coupled lines is designed in [20], in which a wide band and filtering response with high attenuation was obtained. In [21], triangular-shaped open stubs are incorporated in the device's structure in order to present a coupler with rejection band, which achieved a bandwidth of 200 MHz within a main frequency of 700 MHz. A coupler with rectangular open stubs is designed in [22], and achieved filtering response and harmonic rejection. In many designs [23; 24; 25; 26; 27; 28; 29; 30; 31], resonators and filters have been used in the divider structure to suppress harmonics. Applied resonators increase the complexity of circuits, and if resonators are not used properly, they may also increase insertion loss. In [23], a WPD with rectangular stubs and coupled line resonators is presented. The applied resonators in [23] reduced the overall size of the designed WPD. A multi-mode resonator and coupling lines are incorporated int the presented WPD in [25] to achieve a small size and high selectivity. A coupled line, T-shaped resonators, and open stubs are exploited in [26] within the design of a divider; this achieved dual band operation and a filtering response. The presented work in [27] proposes a miniaturized WPD that uses rectangular resonator cells instead of quarter-wave length branches, which reduced the circuit size, increased the bandwidth, and eliminated unwanted harmonics.