Physics-Based Feature Learning for Efficient Data-Driven Compression of Scientific Datasets

Effective lossy compression and development of future post-compression predictive models are key to the success of large scientific computational campaigns. The novel Discontinuous Data-informed Local Subspaces (DDLS) compressor aims to improve upon the existing state-of-the-art data-agnostic compressors by tailoring predictor functions to the target high-fidelity data. This is achieved by learning a dictionary of spatially local features from a small set of representative data and then encoding the target data with the dictionary in a block-wise manner. The choice of the features' spatial span strongly impacts both the compression efficiency and the accuracy of the physics-based quantities of interest. The present study focuses on optimizing the feature learning process by using physics-based metrics rather than trial-and-error methods. We demonstrate that the DDLS approach learns optimal features from a single observation, provided that the observation is carefully selected and the feature span aligns with the key characteristic length scales of the physical system. We consider two canonical problems for demonstration: a two-dimensional incompressible laminar flow past a cylinder for various Reynolds numbers, and a three-dimensional homogeneous and isotropic turbulent flow.