UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression

2026-04-01

AI Summary

This work addresses the challenge of reconstructing high-dimensional spatiotemporal fields from sparse sensor observations, where reliable uncertainty quantification is often lacking—particularly in complex, data-scarce, or highly stochastic systems. The authors propose a novel distribution learning framework based on engression, uniquely integrating it with a shallow recurrent decoder (SHRED). By injecting noise into the input and leveraging single-network resampling, the method efficiently generates well-calibrated predictive distributions without requiring additional network components or retraining, thereby incurring minimal computational overhead. Evaluated on both real-world and synthetic datasets spanning turbulence, atmospheric dynamics, neuroscience, and astrophysics, the approach achieves high-fidelity reconstructions alongside accurate uncertainty estimates. Ablation studies further confirm the contribution of each component to the overall performance.

Abstract

Reconstructing high-dimensional spatiotemporal fields from sparse sensor measurements is critical in a wide range of scientific applications. The SHallow REcurrent Decoder (SHRED) architecture is a recent state-of-the-art architecture that reconstructs high-quality spatial domain from hyper-sparse sensor measurement streams. An important limitation of SHRED is that in complex, data-scarce, high-frequency, or stochastic systems, portions of the spatiotemporal field must be modeled with valid uncertainty estimation. We introduce UQ-SHRED, a distributional learning framework for sparse sensing problems that provides uncertainty quantification through a neural network-based distributional regression called engression. UQ-SHRED models the uncertainty by learning the predictive distribution of the spatial state conditioned on the sensor history. By injecting stochastic noise into sensor inputs and training with an energy score loss, UQ-SHRED produces predictive distributions with minimal computational overhead, requiring only noise injection at the input and resampling through a single architecture without retraining or additional network structures. On complicated synthetic and real-life datasets including turbulent flow, atmospheric dynamics, neuroscience and astrophysics, UQ-SHRED provides a distributional approximation with well-calibrated confidence intervals. We further conduct ablation studies to understand how each model setting affects the quality of the UQ-SHRED performance, and its validity on uncertainty quantification over a set of different experimental setups.

Problem

• uncertainty quantification
• sparse sensing
• spatiotemporal reconstruction
• distributional learning
• sensor measurements

Innovation

• uncertainty quantification
• engression
• shallow recurrent decoder
• sparse sensing
• distributional regression