Analysis of complex engineering systems require the modeling of typically heterogenous physical processes and necessitates a large number of simulations to evaluate the interplay between model, parametric, and process uncertainties on the system dynamics. Construction of surrogate approximations targetting computationally expensive components can help alleviate some of the computational cost associated with forward and inverse workflows for uncertainty quantification and optimization. In this talk we will present a surrogate modeling framework based on functional tensor networks. This approach allows for flexibility in adapting univariate basis functions to input-output maps observed in the computational expensive models thus reducing the number of terms required in the approximation. The tensor network structure can be adapted to mimic the interplay between the subcomponents of the expensive computational model potentially resulting in further savings in the computational cost of building the surrogate models. In this talk we will present surrogate approximations for the land model component of the Energy Exascale Earth System Model (E3SM) and for the mechanical response of polycrystalline media. Efficient tensor algebra will be employed to generate global sensitivity analysis information that can used downstream to inform further model development.