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Predicting the spatiotemporal variation in streamflow along with uncertainty quantification enables decision-making for sustainable management of scarce water resources. Process-based hydrological models (aka physics-based models) are based on physical laws, but using simplifying assumptions which can lead to poor accuracy. Data-driven approaches offer a powerful alternative, but they require large amount of training data and tend to produce predictions that are inconsistent with physical laws. This paper studies a constrained reasoning and learning (CRL) approach where physical laws represented as logical constraints are integrated as a layer in the deep neural network. To address small data setting, we develop a theoretically-grounded training approach to improve the generalization accuracy of deep models. For uncertainty quantification, we combine the synergistic strengths of Gaussian processes (GPs) and deep temporal models (i.e., deep models for time-series forecasting) by passing the learned latent representation as input to a standard distance-based kernel. Experiments on multiple real-world datasets demonstrate the effectiveness of both CRL and GP with deep kernel approaches over strong baseline methods.

Snow Water-Equivalent (SWE) -- the amount of water available if snowpack is melted -- is a key decision variable used by water management agencies to make irrigation, flood control, power generation and drought management decisions. SWE values vary spatiotemporally -- affected by weather, topography and other environmental factors. While daily SWE can be measured by Snow Telemetry (SNOTEL) stations with requisite instrumentation, such stations are spatially sparse requiring interpolation techniques to create spatiotemporally complete data. While recent efforts have explored machine learning (ML) for SWE prediction, a number of recent ML advances have yet to be considered. The main contribution of this paper is to explore one such ML advance, attention mechanisms, for SWE prediction. Our hypothesis is that attention has a unique ability to capture and exploit correlations that may exist across locations or the temporal spectrum (or both). We present a generic attention-based modeling framework for SWE prediction and adapt it to capture spatial attention and temporal attention. Our experimental results on 323 SNOTEL stations in the Western U.S. demonstrate that our attention-based models outperform other machine learning approaches. We also provide key results highlighting the differences between spatial and temporal attention in this context and a roadmap toward deployment for generating spatially-complete SWE maps., Comment: 7 pages, To be published in Proceedings of The Thirty-Sixth Annual Conference on Innovative Applications of Artificial Intelligence (IAAI-24)