In the numerical integration of differential equations, preserving the geometric structure and invariants of the original system is essential. Inspired by Galerkin variational integrators, we propose a new class of methods—nonlinear variational integrators—designed to enable large time-step integration using flexible, nonlinearly parameterized function representations. Unlike classical approaches that approximate generalized coordinates in the (space-)time domain using polynomials, our method employs more general nonlinear function spaces, such as those parameterized by neural networks or other expressive models. The degrees of freedom are determined by the corresponding discrete Euler–Lagrange (field) equations. Like other variational integrators, our approach ensures long-time stability, energy preservation, and a reduction in the number of degrees of freedom required over a given time interval