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

TL;DR

UQ-SHRED is a novel neural network framework that enhances the SHRED architecture by providing uncertainty quantification for sparse sensing in complex systems, with minimal additional computational cost.

Contribution

It introduces a distributional regression approach called engression within SHRED, enabling uncertainty estimation without retraining or extra network structures.

Findings

UQ-SHRED produces well-calibrated confidence intervals on synthetic and real datasets.

The method requires only noise injection at input and no additional training.

Ablation studies reveal how model settings influence uncertainty quantification quality.

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.