PNNL

Abstract

Ensemble simulation and learning (ESnL) have long been used in hydrology to enhance model forecasting skills. However, the computational demands associated with forward simulation and inverse mapping can be substantial when employing process-based models directly. We propose a novel deep neural operator learning approach to tackle this challenge. Deep neural operators are generic deep learning algorithms that can be trained to learn functional mappings between any pair of infinite-dimensional spaces, providing a highly flexible tool for scientific machine learning. Built upon a specific deep neural operator, DeepONet, our integrated workflow aims to address several classical problems in hydrology, namely, streamflow forecasting, parameter estimation, prediction in ungauged basins, and uncertainty quantification. The DeepONet workflow is demonstrated using an existing large model ensemble created for an eastern U.S. watershed, with a total of 10 stream gages. Results suggest DeepONet achieves high efficiency in learning a surrogate model from the model ensemble, with the modified Kling-Gupta Efficiency exceeding 0.9 on test sets. Global parameter estimation using the Generic Algorithm and the trained DeepONet surrogate model also yields robust results. Additionally, we for mulate and train a separate DeepONet model for physics-informed seq-to-seq learning, which is shown to further reduce biases in the pre-trained DeepONet surrogate model. While this study focuses primarily on a single watershed, our framework is general and can be extended to enable learning from model ensembles across multiple basins or models. Thus, this research represents a significant contribution to the application of hybrid machine learning in hydrology.