An Initialization Method for Feedforward Artificial Neural Networks Using Polynomial Bases

We propose an initialization method for feedforward artificial neural networks (FFANNs) trained to model physical systems. A polynomial solution of the physical system is obtained using a mathematical model and then mapped into the neural network to initialize its weights. The network can next be trained with a dataset to refine its accuracy. We focus attention on an elliptical partial differential equation modeled using a feedforward backpropagation network. We present a numerical example and compare our method with other initialization methods. Our method converges nearly 90% faster compared to random weights, with higher probability of convergence to an acceptable local minimum.