Reduced order models are not a new technique and there are numerous applications to fluid flows ranging from laminar two dimensional cases to fully turbulent three dimensional examples. Also in the field of multi body dynamics a modal reduction of flexible bodies is well-established. The application of reduced order models to fully three dimensional and geometrically parametrized solid mechanics problems is a bit less common and especially their integration with auto-diff libraries like Pytorch offers promising perspectives and has not yet been investigated in full detail. The implemented reduced order model is based on a Galerkin projection, where the solution space is derived using a widely accepted POD approach. In order to account for non-affine parametric dependencies w.r.t. geometrical parameters, a hyper-reduction technique similar as initially shown in is applied, allowing the fast assembly of the reduced algebraic system during the so called online phase. The evaluation times of the reduced model are two to three orders of magnitude below the high fidelity model and when comparing the accuracy for predicting scalar target values, the reduced order model yields slightly better scalability for high-dimensional parameter spaces than classical surrogate models (e.g. gaussian process regression). A big advantage of the reduced model is however, that it is more robust to extrapolations outside of the known parametric region and furthermore, that it can be directly used for optimizations where the objective function does not need to be known in advance; this makes the approach quite flexible. The presented model is used to optimize the weight of a three dimensional steel frame while maintaining a certain stiffness. As the model is implemented in Pytorch, the available auto-diff engine can used to calculate the objectives sensitivity w.r.t. the input parameters via backpropagation and a gradient based L-BFGS optimizer is applied to minimize the objective function.