## 1 Introduction
### Literature Review  
Among the key aspects of naval architecture is predicting the resistance of ships and submerged bodies. In this regard, Reynolds Averaged Navier Stokes Equations (_RANS_) based solutions were studied broadly in the literature. [PERSON] et al. [3] compared the results for benchmark vessels investigated by various institutions and universities with codes implementing _RANS_. [PERSON] et al. [4], investigated resistance and wave patterns of a submarine model at different depths, and the influence of free surface on the resistance was discussed. [PERSON] et al. [5] studied flow behavior on a model of an underwater vehicle with a tango-shaped nose and presented some formulas for the resistance of submarine bare hulls in deep water. Lastly, they compared the equation to determine the optimum resistance coefficient for the submarine.  
[PERSON] et al. [6] applied _RANS_-based _CFD_ to the numerical simulation of the flow field around a surface piercing and a fully submerged body to estimate the total resistance of the submarine. A _CFD_ analysis was presented by [PERSON] et al. [7] on the bare hull form of submarines or torpedoes to minimize resistance. They studied the bare hull form without free surface effect since the required power will always be estimated for submerged navigation. _CFD_ was used by [PERSON] [8] to determine the viscous resistance of a tourist submarine suitable for work in the Red Sea region. In that study, the resistance and hydrodynamic characteristics of the flow surrounding the tourist submarine under different speeds were investigated using the finite volume _RANS_ code _CFX_. [PERSON] et al. [9] used model-scale submarine resistance tests to predict full-scale resistance. It was assumed that the residual resistance coefficient is independent of the Reynolds number and is measured at the model-scale.  
[PERSON] et al. [10] evaluated experimentally and numerically the pressure and frictional force in the opposite direction of the mini submarine movement. [PERSON] et al. [11] calculated the resistance coefficient of an exploratory submarine with a displacement of 6.8 tons moving forward, backward, diving, and rising in different directions. A full-scale SUBOFF model was investigated by [PERSON] et al. [12] for different forward speeds, submerged positions, and fluid densities. They showed that the submarine hydrodynamic performance is significantly affected by the forward speed and submerged depth. Based on Star CCM+ fluid simulation software, the resistance coefficients under different submarine depths and speeds were calculated based on the specific resistance characteristics of submarines sailing near the surface by [PERSON] et al. [13].  
Combining physics models with neural networks has been used in fluid dynamics during the last few years [14; 15; 16; 17; 18]. As an example, convolutional neural networks were used by [PERSON] et al. [14] to model the flow around a circular cylinder at 100 Reynolds numbers. [PERSON] et al. [17] used machine learning for advancing fluid mechanics. The authors demonstrated that the suggested model is likely to have a positive impact provided outcomes are held to the long-held critical standards that should guide flow physics research. In another research, [PERSON] et al. [18] reviewed the history and development of machine learning in fluid mechanics, as well as opportunities for the future. A discussion of fundamental machine learning methodologies and their use in understanding, modeling, optimizing, and controlling fluid flow was presented in that paper. The models in these studies were used as a \"black box\" without explicit equations to estimate unknown parameters.