This paper shows how multi-dimensional functions, describing the operation of complex equipment, can be learned. The functions are points in a shape space, each produced by morphing a prototypical function located at its origin. The prototypical function and the space's dimensions, which define morphological operations, are learned from a set of existing functions. New ones are generated by averaging the coordinates of similar functions and using these to morph the prototype appropriately. This paper discusses applying this approach to learning new functions for components of gas turbine engines. Experiments on a set of compressor maps, multi-dimensional functions relating the performance parameters of a compressor, show that it more accurately transforms old maps, into new ones, than existing methods.
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