Mapping polynomial fitting into feedforward neural networks for modeling nonlinear dynamic systems and beyond

This study presents an explicit demonstration on constructing a multilayer feedforward neural network to approximate polynomials and conduct polynomial fitting. Built on an algebraic analysis of sigmoidal activation functions rather than incremental training, this work reveals the capability of the “universal approximator” by relating the “soft computing tool” to an important class of conventional computing tools widely used in modeling nonlinear dynamic systems and many other scientific computing applications. The authors strive to enable physical interpretations and afford full control when applying the highly adaptive, powerful yet subjective neural network approach. This work is a part of the effort of bridging the gap between the black-box and mechanics-based parametric modeling.