A Prediction Model for Neuronal Synaptic Inputs

In this manuscript it is exposed a method to approximate functions using artificial neural networks based on wavelets (wavenet). The focus is on finding the best configuration for the wavenet, from various possible settings in relation to the mathematical development of the network, to be able to approximate a FitzHugh-Nagumo model to later be used to predict any scenario with a single initial condition for the model. It is shown that after training the artificial network, it is able to approximate the non-linear behaviour of the FitzHugh-Nagumo model with high accuracy, providing a neuron model which can be then applied to models for real neurons with similar inputs to those from the wavenet. Finally, it is proved that additional linear terms applied to the outputs improve significantly the error of the approximation to those wavenets with non-linear type scale functions, thus it is been possible to obtain better results without the need to increase the resolution level and thereby reducing the simulation time