A sparse coding approach to up-sampling and extrapolating 2-dimensional computational fluid dynamics simulations

• Main Authors: Wang, Daniel A, Pritchard, Howard, Kenyon, Garrett T
• Format: Conference Proceeding
• Language: English
• Published: SPIE 01.08.2021
• ISBN: 1510645241; 9781510645240
• ISSN: 0277-786X
• DOI: 10.1117/12.2594322

We demonstrate through unsupervised machine learning that spatiotemporal latent representations optimized for sparse coding are able to support up-sampling of decimated frames, interpolation of missing frames, and extrapolation to future frames of computational fluid dynamics (CFD) simulations via linear regression. Specifically, we optimize an overcomplete bases of convolutional kernels for the sparse reconstruction of local x,y,z velocities, which are then inferred from decimated data streams and used to reconstruct the entire stream. The input data we use here is a series of time steps extracted as 2D slices from 3D CFD simulations. The simulation input is decimated by removing every-other pixel in every odd frame and by removing every even frame entirely, resulting in a 75% decimation that exposes the sparse coding model to only 25% of the original data. Reconstructions generated by sparse inference utilize features that capture higher-order structures using a Locally Competitive Algorithm to learn the corresponding physics. The quality of reconstructions against the original data can be quantified by the absolute difference between pixels via PSNR in which a higher score indicates a reconstruction that is more faithful to the original input. This study observes the up-sampled, interpolated, and extrapolated reconstructions compared against their inputs for both 4-frame, 6-frame, and 8-frame architecture. Our results suggest that sparse coding networks may offer a competitive method for up-sampling, interpolating and extrapolating from lower to higher resolution CFD simulations.