For microstructured materials with non-periodic cells or non-separated scales, such as additively manufactured lattices and metamaterials, multiscale modeling approaches are inapplicable, but full-scale simulations are still prohibitively time-consuming, in particular for nonlinear materials and large deformations. For a fast and efficient nonlinear simulation of such structures, similar to [1], we introduce the concept of surrogate elements, which capture the effective mechanical behavior of the unit cells of the microstructure only through the boundary nodes. We consider an internal energy potential, which enables the determination of the energy and (generalized) forces associated with a given deformation of the microstructure's boundary nodes. This potential is represented by feed-forward neural network (FFNN) that incorporates energy conservation, invariance to rigid body translations and rotations, normalization conditions, and parameter variations of the unit cells, i.e., through physics-enhanced machine learning. The equilibrium configuration of a macro-structure consisting of many interconnected unit cells can then be obtained by minimizing the total potential energy, which is assembled from the microstructure potentials. Here, this concept is demonstrated in application to 2D and 3D beam lattice microstructures. First, a data set for the surrogate potential, forces, and moments is build by performing nonlinear simulations of lattice unit cells subject to different deformation and load cases. Then, a physics-enhanced neural network is trained on this data in order to approximate the functional relationship for the energy potential. We aim to demonstrate the accuracy, efficiency and robustness of the approach through several verification examples, in which these surrogate potentials are applied for the nonlinear simulation of macro-structures. [1] G. Capuano and J. J. Rimoli. “Smart Finite Elements: A Novel Machine Learning Application”. Computer Methods in Applied Mechanics and Engineering 345:363–381 (2019)