CS-SHRED: enhancing SHRED for robust recovery of spatiotemporal dynamics

Abstract We present CS-SHRED, a novel deep learning architecture that integrates compressed sensing (CS) into a shallow recurrent decoder (SHRED) to reconstruct spatiotemporal dynamics from incomplete, compressed or corrupted data. Our approach introduces two key innovations. First, by incorporating CS techniques into the SHRED architecture, our method leverages a batch-based forward framework with ℓ1 regularization to robustly recover signals even in scenarios with sparse sensor placements, noisy measurements and incomplete sensor acquisitions. Second, an adaptive loss function dynamically combines mean squared error (MSE) and mean absolute error (MAE) terms with a piecewise signal-to-noise ratio (SNR) regularization, which suppresses noise and outliers in low-SNR regions while preserving fine-scale features in high-SNR regions. We validate CS-SHRED on challenging problems, including viscoelastic fluid flows, maximum specific humidity (qmax) fields, sea surface temperature (SST) distributions and rotating turbulent flows. Compared to the traditional SHRED approach, CS-SHRED achieves significantly higher reconstruction fidelity—as demonstrated by improved structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) values, lower normalized errors and enhanced learned perceptual image patch similarity (LPIPS) scores—thereby providing superior preservation of small-scale structures and increased robustness against noise and outliers. Our results underscore the advantages of the integrated CS-SHRED design, in which CS recovery is embedded into the recurrent reconstruction pipeline with a long short-term memory (LSTM) sequence model for characterizing temporal evolution and a shallow decoder network for modelling the high-dimensional state space. The SNR-guided adaptive loss function for spatiotemporal data recovery establishes CS-SHRED as a promising tool for a wide range of applications in environmental, climatic and scientific data analyses.