  Multiscale modeling is a systematic approach to describe the behavior of
complex systems by coupling models from different scales. The approach has been
demonstrated to be very effective in areas of science as diverse as materials
science, climate modeling and chemistry. However, routine use of multiscale
simulations is often hindered by the very high cost of individual at-scale
models. Approaches aiming to alleviate that cost by means of Gaussian process
regression based surrogate models have been proposed. Yet, many of these
surrogate models are expensive to construct, especially when the number of data
needed is large. In this article, we employ a hierarchical sparse Cholesky
decomposition to develop a sparse Gaussian process regression method and apply
the method to approximate the equation of state of an energetic material in a
multiscale model of dynamic deformation. We demonstrate that the method
provides a substantial reduction both in computational cost and solution error
as compared with previous methods.
