Application of Extreme Learning Machines for Modeling Wind in Energy-Optimal Routing Problems

Ultra long endurance flight of unmanned aircraft is now possible over multiple days. However, pushing endurance to its limits requires an energy optimal routing problem to be solved. This problem relies on an accurate description of the wind field in order to find the route that best leverages tail winds while also avoiding head winds. The wind field is provided in the form of a large dimensional data table compiled from various predictive models, and is typically implemented by linearly interpolating over the data. To reduce the data footprint and to provide smooth wind derivatives (as required by the optimization task), this paper explores the use of extreme learning machines (ELM) to create surrogate models of the wind field that both reduce data storage requirements and improve computational efficiency. This is due to the ability of the ELM to compress the raw data through its neural encoding and to perform inference as a series of matrix-matrix computations, rather than N-dimensional interpolation. The results show that an ELM network can be trained to represent a practical wind field dataset in only seconds but with accuracy that is sufficient to support the solution of the energy optimal routing problem in terms of a BVP derived using Pontryagin's Minimum Principle.