The project seeks to develop new computational methods for compressing streamed tensor data.  The methods will be adaptive, efficient, reliable and general-purpose.  Motivated by the ubiquity of tensorial datasets that are too large to store, the project aims to achieve dramatic compression of tensor streams through low-rank tensor decompositions, and more generally data-sparse tensor representations.  Driving science applications include numerical simulations of fluid flows and other nonlinear evolution equations; as well as 3D reconstruction in high-throughput imaging, especially X-ray free electron lasers (XFEL).

Mathematically, the key hypothesis is that randomized linear projections provide an approach to data reduction that is well-suited to maintaining data-sparse representations of tensors from large data streams.  Within this framework, the PIs will develop two novel computational frameworks for streamed tensor compression.  The first is to maintain global "sketches" of the data stream for use within iterative optimization algorithms, like alternating least squares methods.  The second is to build algorithms that exploit structure in previous sketches to reduce the amount of information that needs to be stored.  The PIs will combine ideas from randomized embeddings with randomized sampling techniques to construct methods that are both exceptionally fast and highly reliable.  Randomized a posteriori error estimators will be incorporated to ensure that the compressed representations are accurate to within a requested precision.  The new tools will lend themselves to modern massively parallel and distributed computing architectures.