CS-SHRED: Enhancing SHRED for Robust Recovery of Spatiotemporal Dynamics

We present $\textbf{CS-SHRED}$, a novel deep learning architecture that integrates Compressed Sensing (CS) into a Shallow Recurrent Decoder ($\textbf{SHRED}$) to reconstruct spatiotemporal dynamics from incomplete, compressed, or corrupted data. Our approach introduces two key innovations. First, by incorporating CS techniques into the $\textbf{SHRED}$ 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.