Chapter 7 - AI for physics-inspired hydrology modeling

Abstract

In this chapter, we walk from beginning to end of how to implement the so-called “hybrid” models that blend machine learning with traditional modeling techniques for simulating the hydrologic cycle. Specifically, this chapter outlines the basics of automatic differentiation, and its use in optimization and machine learning. Then, we cover some basic background on numerical optimization. These pieces all come together in a proof-of-concept example for parameterizing very simple differential equations with neural networks to represent unknown relationships. We present a synthetic example describing reservoir behavior to illustrate the techniques. Following this, we show how these techniques can be scaled from synthetic data to a real hydrologic model. The model that we implement has multiple soil storage components, vegetation, and is represented by a well-understood set of differential equations. We use the techniques built up through the course of the chapter to practically show how to fuse machine-learning techniques with more traditional techniques in a way that is physically consistent and interpretable.