  We propose a strategy to compress and store large volumes of scientific data
represented on unstructured grids. Approaches utilizing tensor decompositions
for data compression have already been proposed. Here, data on a structured
grid is stored as a tensor which is then subjected to appropriate decomposition
in suitable tensor formats. Such decompositions are based on generalization of
singular value decomposition to tensors and capture essential features in the
data with storage cost lower by orders of magnitude. However, tensor based data
compression is limited by the fact that one can only consider scientific data
represented on structured grids. In case of data on unstructured meshes, we
propose to consider data as realizations of a function that is based on
functional view of the tensor thus avoiding such limitations. The key is to
efficiently estimate the parameters of the function whose complexity is small
compared to the cardinality of the dataset (otherwise there is no compression).
Here, we introduce the set of functional sparse Tucker tensors and propose a
method to construct approximation in this set such that the resulting compact
functional tensor can be rapidly evaluated to recover the original data. The
compression procedure consists of three steps. In the first step, we consider a
fraction of the original dataset for interpolation on a structured grid
followed by sequentially truncated higher order singular value decomposition to
get a compressed version of the interpolated data.We then fit singular vectors
on a set of functional basis using sparse approximation to obtain corresponding
functional sparse Tucker tensor representation. Finally, we re-evaluate the
coefficients of this functional tensor using randomized least squares at a
reduced computational complexity. This strategy leads to compression ratio of
orders of magnitude on combustion simulation datasets.
