PolyNet: A Polynomial-Based Learning Machine for Universal Approximation

Currently, there is a need in all disciplines for efficient and powerful machine learning (ML) algorithms for handling offline and real-time nonlinear data. Industrial applications abound from real-time control systems to modeling and simulation of complex systems and processes. Certain ML methods have become popular with researchers and engineers. Such techniques include fuzzy systems (FSs), artificial neural networks (ANNs), radial basis function (RBF) networks, and support vector regression (SVR) machines. Historically, polynomial-based learning machines (PLMs) based on the group method of data handling (GMDH) model have enjoyed usage similar to that of these other methods. However, unwieldy kernel functions in the form of large high-order polynomials, and relatively limited computer speed and capacity, have limited the use of PLMs to comparatively small problems with low dimensionality and simple functional relationships. Thus, true polynomial-based ML solutions have drifted out of vogue for at least two decades. This work attempts to reinvigorate the interest in PLMs by introducing a novel practical implementation called PolyNet. It will be shown that once certain algorithms are applied to the generation, training, and functional operation of PLMs, they can compete on par with or better than methods currently in use.