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.

翻译：从稀疏传感器测量中重建高维时空场在许多科学应用中至关重要。浅层递归解码器（SHRED）架构是一种最新的先进架构，能从超稀疏传感器测量流中重建高质量的空间域。SHRED的一个重要局限在于，对于复杂、数据稀缺、高频或随机系统，时空场的一部分必须以有效的不确定性估计进行建模。我们引入了UQ-SHRED，一种针对稀疏感测问题的分布学习框架，通过一种基于神经网络的分布回归方法——engression——提供不确定性量化。UQ-SHRED通过学习以传感器历史为条件的空间状态预测分布来对不确定性进行建模。通过在传感器输入中注入随机噪声，并使用能量评分损失进行训练，UQ-SHRED以最小的计算开销生成预测分布，仅需在输入处注入噪声并通过单一架构进行重采样，无需重新训练或额外的网络结构。在包括湍流、大气动力学、神经科学和天体物理学在内的复杂合成和真实数据集上，UQ-SHRED提供了具有良好校准置信区间的分布近似。我们进一步进行了消融研究，以理解每个模型设置如何影响UQ-SHRED性能的质量，及其在一组不同实验设置下对不确定性量化的有效性。