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 $\ell_1$ 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 fields, sea surface temperature distributions, and rotating turbulent flows. Compared to the traditional SHRED approach, CS-SHRED achieves significantly higher reconstruction fidelity -- as demonstrated by improved SSIM and PSNR values, lower normalized errors, and enhanced LPIPS scores-thereby providing superior preservation of small-scale structures and increased robustness against noise and outliers. Our results underscore the advantages of the jointly trained CS and SHRED design architecture which includes an LSTM sequence model for characterizing the temporal evolution with a shallow decoder network (SDN) for modeling the high-dimensional state space. The SNR-guided adaptive loss function for the spatiotemporal data recovery establishes CS-SHRED as a promising tool for a wide range of applications in environmental, climatic, and scientific data analyses.