Argonne used compressive techniques from image processing to identify compressed subspaces that preserve the accuracy of full-order measurements of geophysical fields, such as those arising from the National Oceanic and Atmospheric Administration (NOAA) Sea-Surface Temperature and National Aeronautics and Space Administration (NASA) Daymet. Using these subspaces, we tracked the evolution of the full-order fields and built forecasting models that are orders of magnitude faster than their partial differential equation-based counterparts.

We identified the compressed subspaces by using the principal components of the full-order field snapshots, as well as by using convolutional autoencoders to test the effect of linear and nonlinear compression, respectively. Our time-series models within latent space utilize recurrent neural networks to learn memory-embedded kernels for temporal trajectories mapped into the reduced-space. We observed significant reductions in the degrees-of-freedom and time-to-forecast, resulting in new possibilities for data assimilation and ensemble forecasting.