The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relation which often involves many independent variables. The constitutive relation of a polymeric fluid is a function of six variables, even after making the simplifying assumption that stress depends only on the rate of strain. Precomputing such a function is usually considered too expensive. Consequently the value of sequential multiscale modeling is often limited to "parameter passing". Here we demonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many variables. This strategy dramatically increases the efficiency of sequential multiscale modeling, making it very competitive in many situations.