Multilevel techniques for compression and reduction of scientific data-quantitative control of accuracy in derived quantities

Although many compression algorithms are focused on preserving pointwise values of the data, application scientists are generally more concerned with derived quantities. Equally well, the user may even be willing to accept a high level of lossiness in the compression provided that the compressed data respect certain invariants, such as mass conservation. In the current work, we develop a mathematical framework and techniques that enable data to be adaptively compressed while maintaining a specified tolerance on a class of user-prescribed quantities. The algorithm is used to augment the functionality of the data reduction package MGARD developed in previous work and the functionality is illustrated by a range of application including data from computational simulation of autocatalytic reaction simulation, turbulent combustion simulation, experimental data obtained from magnetic confinement fusion experiment, and simulation of turbulent flow along a rectangular channel. In each case, we consider one or more relevant quantities of interest and reduce the data so as to preserve these quantities.