## 1 Introduction
On the other hand, the mathematical and numerical approach relies on the use of generic equations or simulations to study different deposition scenarios and see the influence of the layer geometry on the final produced part [18; 19; 20; 21; 22; 23]. To improve the surface quality of the deposition [PERSON] et al. [24] investigated the influence of varying the laser's power and defocusing distance on deposition. The laser power was decreased at each layer to avoid energy accumulation and reduce the pool size change. Additionally, the same layer thickness was used. This approach yields differences in the top layer when changing defocusing distances due to fluctuating parameters and system error. This is due to the height difference observed between layers, which propagate to the other layers, becoming increasingly pronounced if the difference is not compensated for, hence, the necessity of self-regulating deposition height. As layer thickness needs to be adjusted to satisfy the process's growth, [PERSON] et al. [25] proposed a reconstruction of the spatial map of the height to see the variation of the layer thickness and found a self-regulating mechanism therein; after an initial transient period showing faster deposition growth in the first layers, deposition rate exhibits a decreasing trend until converging to steady-state, interpreted as an equilibrium condition, is achieved. In this approach, although there exist disturbances from system sensitivity and error, the self-regulating mechanism occurring during the deposition process is obvious. For this reason, the problem of height prediction should be solved in advance of regulating those process parameters occupying a primary level in the 3D printing process. Machine learning (ML) is applied in many domains, today. Many industrial sectors face new research challenges and complex problems yet to be addressed. The advantage of ML is demonstrated in areas where underlying physical models are difficult to express. The neural network (NN) algorithm is the most used ML method due to its advanced algorithm structure [26]. NNs can be used as supervised ML or unsupervised learning problems for complex problems with highly nonlinear relationships. The architecture of an NN consists of the input layer, a hidden layer, and an output layer [27]. The layers are composed of nodes or neurons. In [PERSON] et al. [28], an improved artificial neural network (ANN) using arithmetic optimization algorithm (IANN-AOA) for damage quantification problems is proposed. Free vibration and damage identification have been investigated on functionally graded material (FGM) plates, while, in [29], damaged laminated composite structures are identified using an ANN. In this approach, the network is trained using fast convergence speed of gradient descent (GD) techniques and the global search capacity of evolutionary algorithms EAs is used to quickly guarantee the best possible solution. Finally, [PERSON] et al. [30] implemented a modified transmissibility damage indicator using local frequency response ratio (LFCR) and ANN to detect the location and size of damage in composite structures while reducing collected data for fast prediction and high accuracy. Recently, researchers have worked on the bead geometry prediction models using machine learning approaches to address issues relating to deposition accuracy [7; 31; 32; 33; 34; 35]. [PERSON] et al. [31] used second-order regression with a neural network for predicting bead ge ometry in wire and arc additive manufacturing (WAAM) to study the relationship between the process variables and the final bead geometry. While [PERSON] and [PERSON] [32] used the back propagation (BP) neural network model for estimating bead geometry for tungsten inert gas (TIG) welding process. [PERSON] et al. [7] developed a roughness measuring method for arc additive manufacturing using a laser sensor-based approach combined with different machine learning models. On the other hand, [PERSON] et al.