This paper presents an approach for creating tensor product (TP) models based on sparse or non-uniform samples representing arbitrary datasets, and for manipulating the resulting TP structure to further identify the models behind the datasets. Given the usefulness of TP models in merging together closed algebraic formulae and tensor representations, it is argued that the proposed approach can be applied towards understanding the underlying complexity of a given dataset, while iteratively arriving at a model for the process that generated it. The key idea behind the approach is demonstrated using a dataset on sound pressure levels generated by different-sized airfoils in a wind tunnel.