Traditional constitutive model calibration solves an inverse problem using optimization [1]. This requires multiple evaluations of physics simulations of material characterization tests; the results of which are compared to experimental data to form an objective for minimization. Depending on material model complexity and the characterization tests required to parameterize it, the computational expense of calibrations can be prohibitive. Surrogate-based optimization techniques use a surrogate of the objective function [2] or surrogates that predict outputs of physics simulations [3] to reduce the computational burden of optimization. Issues with surrogate-based optimization include the curse-of-dimensionality, difficulty creating global surrogates for nonlinear models and difficulty in selecting appropriate surrogates [2,3]. We propose sparse grid surrogates that predict vector responses for material characterization test simulations. Surrogate training occurs independent of the constitutive model calibration, allowing surrogate reuse for follow-on calibrations where applicable. The proposed surrogates are valid for a single material characterization test over a predetermined parameter space for a specific material model. To support material models with up to 10 parameters over a large range of parameter values, we use surrogates that are trained adaptively. Training and validating the surrogate over a large parameter range in the parameter space promotes reuse of the surrogates for calibrating similar materials. We assess the effectiveness of the surrogates through calibration of constitutive models for aluminum. We generate surrogates for finite element simulations of characterization tests used to calibrate a model with isotropic hypoelasticity, a Hill yield surface and Voce hardening. The surrogates are trained over a parameter space for the model that is generally valid for structural aluminums. We perform calibrations to aluminum characterization data using both surrogates and finite element simulations. The calibration results are compared quantitatively to validate surrogate performance. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.