Over the past few years, the use of artificial intelligent, in particular neural networks (NNs), has gained interest within the aerospace industry to explore and accelerate the aircraft structural design. However, the high amount of data, normally required and sometimes the lack of robustness, have prevented higher adoption. A promising approach to overcome these difficulties is to include methodologies that effectively capture the physics governing the structural problem within the NNs. This work presents the development of an energy-based methodology and a physics-based neural network (PBNN) to predict quickly and accurately the skin effective width of a metallic fuselage panel under hoop tension loads and so to improve and speed up the fuselage sizing, certification and/or optimisation process. First, the energy-based methodology was developed. The fuselage panel was modelled as a cylindrical shallow shell with longitudinal and transverse stiffeners with simply supported or clamped boundary conditions. The stiffeners were modelled as beams and located at the middle plane of the shell. The problem was formulated using thin shell theory and solved by the Rayleigh-Ritz method. Results were compared against exact and approximate solutions from the literature and detailed finite element models (DFEMs) showing excellent correlation. Second, a PBNN that used the skin effective width computed by the energy-based methodology as an additional input feature, was developed to enhance the training of the NN, resulting in a more robust and accurate NN. The proposed PBNN architecture was compared against a traditional NN. A sensitivity analysis was also carried out to test the generalization capacity against changes in the input geometrical variables including extrapolation. Results show excellent predictions of the PBNNs using the energy-based methodology when compared against DFEM