Kinematically exact rod models were a major breakthrough to evaluate complex frame structures undergoing large displacements and the associated buckling modes. However, they are limited to the analysis of global effects, since the underlying kinematical assumptions typically take into account only cross-sectional rigid-body motion and ocasionally torsional warping. For thin-walled members, local effects can be notably important in the overall behavior of the rod. In the present work, high-fidelity simulations using elastic 3D-solid finite elements are employed to provide input data to train a Deep Neural Newtork-(DNN) to act as a surrogate model of the rod’s constitutive equation. It is capable of indirectly representing local effects such as web/flange bending and buckling at a stress-resultant level, yet using only usual rod degrees of freedom as inputs, given that it is trained to predict the internal energy as a function of generalized rod strains. A series of theoretical constraints for the surrogate model is elaborated, and a practical case is studied, from data generation to the DNN training. The outcome is a successfully trained model for a particular choice of cross-section and elastic material, that is ready to be employed in a full rod/frame simulation.