Streamflow Prediction with Uncertainty Quantification for Water Management: A Constrained Reasoning and Learning Approach

TL;DR

This paper introduces a constrained reasoning and learning approach that integrates physical laws into deep neural networks for streamflow prediction, enhancing accuracy and uncertainty quantification in water management.

Contribution

It develops a novel CRL method incorporating physical constraints into deep models and combines Gaussian processes with deep kernels for improved uncertainty estimation.

Findings

CRL improves prediction accuracy with limited data.

Deep kernel GPs enhance uncertainty quantification.

Method outperforms baseline models on real datasets.

Abstract

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.