Neural Network Initialization for Modeling Nonlinear Functions in Engineering Mechanics

This paper introduces a heuristic methodology for designing multilayer feedforward neural networks to be used in modeling nonlinear functions in engineering mechanics applications. It is well recognized that a perfect way to decide an appropriate architecture and assign initial values to start neural network training has yet to be established. This might be because such a challenging issue can only be properly addressed by looking into the features of the function to be approximated and thus might be hard to tackle in a general sense. Here the authors do not intend to provide an exhaustive solution to how to set up multilayer feedforward neural networks to approximate an arbitrary function, rather the focus is given to several significant domain function approximation problems in order to showcase the usefulness and efficiency of the proposed methodology. In a series of previous explorations [15, 17, 18, 19], the governing physics and mathematics of nonlinear hysteretic dynamics and the strength of the sigmoidal basis function were exploited to answer the questions of how (in terms of neural network architecture, e.g., the number of hidden nodes in a universal approximator) and where (in terms of the initial values of weights and biases). In this study, training examples are presented to demonstrate and validate the proposed initial design methodology. Future work is also identified.