The application of Artificial Intelligence techniques, particularly neural networks, to aerospace structural processes has gained significant attention in recent years. However, widespread adoption has been limited due to the intrinsic complexity of structural analysis processes involving multiple variables problems linked by non-linear interaction between them. This challenge can be effectively addressed by integrating physics-based methods directly into the neural network architecture and feature design. This work presents the development of a multi-fidelity neural network (MFNN) architecture to predict quickly and accurately the Global Buckling Reserve Factor (RF) of a composite stiffened panel under combined loads. A two-step multi-fidelity approach is developed: First, a simplified physical model (a Rayleigh-Ritz approximation) is replaced by a Physics-based Neural Networks (PbNNs). This low-fidelity model is capable of handling a wide range of geometries, load cases, and materials with high accuracy and computational speed. Second, a subsequent Neural Network (NN) is developed, which takes the RF from previous PbNN, and other relevant variables (i.e. panel width) as inputs. This final NN covers the gap between the idealizations and the real structure (i.e. panel asymmetry), and incorporates material-specific allowable values, forming the high-fidelity model. The results are compared with Airbus Methodologies, and with a data-based NN showing good correlation. Additionally, sensitivity analysis is also carried out to test the generalization capacity against changes in the input geometrical variables, including extrapolation. Additionally, the MFNN requires less high-fidelity simulations that the data-based NN for the same accuracy.