Practical Considerations in Applying Compressed Sensing to Simulation Data

The move toward exascale computing for scientific simulations is placing new demands on compression techniques. It is expected that the I/O system will not be able to support the volume of data that will be written out. To enable quantitative analysis and scientific discovery, we need techniques that can compress high-dimensional simulation data with near-perfect reconstruction. In this work, we investigate Compressed Sensing (CS) to reduce the size of the data from a fusion simulation of a tokamak in 3 dimensions (Figure (a)). The computational domain of the simulation is a toroid, composed of 32 poloidal planes (shown in blue). Each plane has nearly 600,000 grid points, arranged irregularly, and distributed across multiple processors of a massively parallel system. Since these data are analyzed to understand the behavior of coherent structures (Figure (b)) over time, it is important that these structures remain unchanged after reconstruction using CS. We conducted several experiments to understand how best to apply CS to our data set. We used several metrics to investigate the effects of preprocessing, including scaling to improve the contrast in the data and thresholding to increase the sparsity. To determine the size of the compressed data that would enable near-perfect reconstruction, we evaluated the quality of reconstruction (shown in Figures (c) and (d) using the R2 metric) as we varied the percentage of compression (m/n) for various levels of sparsity (k/n) in the data. We found that a successful application of CS is bounded by the percentage of sparsity in the data - the data have to be sparse enough for compression using CS, but not so sparse that it is more cost effective to just write out the locations and values of the non-zero data points. Our experiments also indicated that scaling the data is very helpful and thresholding helps both with compression and the coherent structure analysis performed on the data.