Neural Net Characterization of Geophysical Processes with Circular Dependencies

This paper describes a method for training neural nets to learn circular dependencies. Variables with circular structure (e.g. time of day, day of year, and earth location) appear in many different contexts within geoscience and remote sensing. Some common representations of circular variables (e.g. time of day in hours) can introduce discontinuities or topological distortions in estimation problems. They do not necessarily prevent a neural net from learning a relationship with circular dependencies. However, using topologically appropriate representations of circular variables can reduce the complexity necessary for a neural net to accurately learn such a relationship despite possibly increasing the number of inputs, and reducing the complexity results in shorter training times. In this paper, neural nets are trained to learn a function of time of day and a function of geolocation. In both examples, using topologically appropriate representations of time and geolocation instead of conventional representations as inputs significantly reduced RMS errors. This issue could be important in global earth science remote sensing applications where significant diurnal, seasonal, or geographical variations exist. The studies presented also suggest the development of a more general framework for training neural networks that considers the topology of variables.