A note on rapid genetic calibration of artificial neural networks

Abstract

Artificial Neural Nets (ANN) have received huge attention in the scientific community over the last decade and are based on layered input-output type frameworks that are essentially adaptive nonlinear regressions of the form ${{{\mathcal {O}}}}={{{\mathcal {B}}}}({\varvec{I}},{\varvec{w}})$, where ${{{\mathcal {O}}}}$ is a desired output and ${{{\mathcal {B}}}}$ is the ANN comprised of (1) synapses, which multiply inputs ($I_1, I_2, \ldots , I_M$) by weights ($w_1, w_2,\ldots , N$) that represent the input relevance to the desired output, (2) neurons, which aggregate outputs from all incoming synapses and apply activation functions to process the data and (3) training, which calibrates the weights to match a desired overall output. A primary issue with ANN is the calibration of the synapse weights. This calibration can be cast as a nonconvex optimization problem, whereby the cost/error function represents the normed difference between observed data and the output of the ANN for a selected set of weights. The objective is to select a set of weight which minimizes the cost/error. One family of methods that are extremely well-suited for this process are genetic-based machine-learning algorithms. The goal of this short communication is to illustrate this process on a clear model problem.