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

2025-07-29

AI Summary

To address spatiotemporal dynamic reconstruction under sparse sampling, noise corruption, and data missing, this paper proposes an end-to-end framework integrating compressed sensing with shallow recurrent decoding. Methodologically, it introduces an SNR-guided adaptive loss function that jointly optimizes MSE, MAE, and piecewise SNR regularization—enhancing denoising in low-SNR regions while preserving fine details in high-SNR regions. It further combines LSTM-based sequential modeling with a lightweight decoder regularized by ℓ₁-norm, enabling efficient reconstruction within a batch-wise forward inference scheme. Evaluated on diverse complex physical fields, the method significantly outperforms SHRED: SSIM and PSNR improve by over 8%, normalized error decreases by 12%, and LPIPS improves by 15%. Notably, recovery accuracy and robustness for small-scale structures are substantially enhanced.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Learning on the Edge & Model Compression
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We present $ extbf{CS-SHRED}$, a novel deep learning architecture that integrates Compressed Sensing (CS) into a Shallow Recurrent Decoder ($ extbf{SHRED}$) to reconstruct spatiotemporal dynamics from incomplete, compressed, or corrupted data. Our approach introduces two key innovations. First, by incorporating CS techniques into the $ extbf{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 $ extbf{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 $ extbf{SHRED}$ approach, $ extbf{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 $ extbf{CS-SHRED}$ as a promising tool for a wide range of applications in environmental, climatic, and scientific data analyses.

Problem

• Recover spatiotemporal dynamics from incomplete or corrupted data
• Enhance robustness in sparse, noisy, and incomplete sensor scenarios
• Improve reconstruction fidelity for environmental and climatic data

Innovation

• Integrates Compressed Sensing into Shallow Recurrent Decoder
• Uses adaptive loss combining MSE, MAE, SNR regularization
• Employs LSTM and shallow decoder for spatiotemporal modeling