Discovering Differential Equations from Earth Observation Data

Abstract

Modeling and understanding the Earth system is a constant and challenging scientific endeavour. When a clear mechanistic model is unavailable, complex or uncertain, learning from data can be an alternative. While machine learning has provided excellent methods for detection and retrieval, understanding the governing equations of the system from observational data seems an elusive problem. In this paper we introduce sparse regression to uncover a set of governing equations in the form of a system of ordinary differential equations (ODEs). The presented method is used to explicitly describe variable relations by identifying the most expressive and simplest ODEs explaining data to model relevant components of the biosphere.