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.

Optimal allocation of agricultural water in the event of droughts is an important global problem. In addressing this problem, many aspects, including the welfare of farmers, the economy, and the environment, must be considered. Under this backdrop, our work focuses on several resource-matching problems accounting for agents with multi-crop portfolios, geographic constraints, and fairness. First, we address a matching problem where the goal is to maximize a welfare function in two-sided markets where buyers' requirements and sellers' supplies are represented by value functions that assign prices (or costs) to specified volumes of water. For the setting where the value functions satisfy certain monotonicity properties, we present an efficient algorithm that maximizes a social welfare function. When there are minimum water requirement constraints, we present a randomized algorithm which ensures that the constraints are satisfied in expectation. For a single seller--multiple buyers setting with fairness constraints, we design an efficient algorithm that maximizes the minimum level of satisfaction of any buyer. We also present computational complexity results that highlight the limits on the generalizability of our results. We evaluate the algorithms developed in our work with experiments on both real-world and synthetic data sets with respect to drought severity, value functions, and seniority of agents.

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.