Machine Learning and Projection-Based Model Reduction in Hydrology and Geosciences

Our world has been facing a number of serious challenges in the past few decades, such as an increased rate of energy and water consumption, climate change, and natural hazards, that have led to complex human-resource dynamics, requiring hydrologists and geoscientists to consider interdisciplinary approaches. The multi-scale and multi-physics nature of these problems have created high-dimensional equations, or processes whose governing equations are not known accurately, making traditional approaches that are based on modeling and solving the physical processes directly, computationally very demanding or inaccurate. Furthermore, many processes in hydrology and geoscience involve solving inverse problems, due to parameters that are either difficult or impossible to measure directly. Inverse problems typically require running of forward solvers many times, aggravating already existing computational issues. This chapter discusses how data-driven approaches can be used to address these challenges. In particular, reduced order modeling (ROM) can be used to capture the most prominent features present in high-dimensional data efficiently, creating fast forward and inverse solvers of physical processes. Further, computational speed-up and increase in the accuracy is achievable by combining ROMs with deep learning techniques