[2604.01305] UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression

Computer Science > Machine Learning arXiv:2604.01305 (cs) [Submitted on 1 Apr 2026] Title:UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression Authors:Mars Liyao Gao, Yuxuan Bao, Amy S. Rude, Xinwei Shen, J. Nathan Kutz View a PDF of the paper titled UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression, by Mars Liyao Gao and 4 other authors View PDF HTML (experimental) 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 computa...