A Hybrid Training Algorithm for Continuum Deep Learning Neuro-Skin
  Neural Network
In this brief paper, a learning algorithm is developed for Deep Learning
NeuroSkin Neural Network to improve their learning properties. Neuroskin is a
new type of neural network presented recently by the authors. It is comprised
of a cellular membrane which has a neuron attached to each cell. The neuron is
the cells nucleus. A neuroskin is modelled using finite elements. Each element
of the finite element represents a cell. Each cells neuron has dendritic fibers
which connects it to the nodes of the cell. On the other hand, its axon is
connected to the nodes of a number of different neurons. The neuroskin is
trained to contract upon receiving an input. The learning takes place during
updating iterations using sensitivity analysis. It is shown that while the
neuroskin cannot present the desirable response, it improves gradually to the
desired level.
Mehrdad Shafiei Dizaji
# A Hybrid Training Algorithm for Continuum Deep Learning Neuro-Skin Neural Network

###### Abstract

In this brief paper, a learning algorithm is developed for Deep Learning Neuro-Skin Neural Network to improve their learning properties. Neuroskin is a new type of neural network presented recently by the authors. It is comprised of a cellular membrane which has a neuron attached to each cell. The neuron is the cell's nucleus. A neuroskin is modelled using finite elements. Each element of the finite element represents a cell. Each cell's neuron has dendritic fibers which connects it to the nodes of the cell. On the other hand, its axon is connected to the nodes of a number of different neurons. The neuroskin is trained to contract upon receiving an input. The learning takes place during updating iterations using sensitivity analysis. It is shown that while the neuroskin cannot present the desirable response, it improves gradually to the desired level.

Neuro-skin, Hybrid Algorithm, Particle Swarm Optimization (PSO), L-BFGS-B Algorithm, Training, Neural Networks, Finite Element.

## 1 Introduction

_Neuro-Skins or Nero-Membranes (NMs)._ In the previous paper, neuroskins are presented and their response characteristics are studied [1]. Neuroskins are an improved version of Dynamic Plastic Neural Networks (DPNN)s which have recently been introduced by the authors [1-2]. As opposed to a DPCNN which contains a limited number of neurons, each of which is only connected to a small number of points of the base medium, a neuro-skin has the property that every small segment of it has the properties of a neuron. In this regard, the neuro-skin can be considered as a homogeneous skin. This property of the neuro-skin is holographic and does not change with the size of the segment taken out of the membrane. This property will be discussed more in the next sections. The membrane exhibits the activation of neurons. That is at any point it issues an output which is a function of the response of the plate at that point. A more general neuro-membrane can be considered which has the property that its output at any point is a function of the membrane response at farther points as well.

While mathematical modelling and analytical study of neuro-membranes is important to formulate the underlying equations governing their behavior and properties, a first numerical study of their dynamic behavior is essential to provide more insight into their behaviour and to visualize their characteristics. To get more information about the neuroskin neural networks and their characteristics, reader can refer to the previous research [1]. The neuro-membrane utilizing in this paper is a two-dimensional plate which has been studied by the authors in their previous papers on DPCNNs [1] - [26]. They have used this problem in all their studies so that the results and characteristics of the different continuous neural network models could be compared. Figure 1 shows the plate which is 500 mm by 1000 mm. It is unrestricted on three of its edges but restricted by 11 simple supports on its fourth edge [1]. The simple supports provide a large number of redundancies in addition to the reactions needed for the static equilibrium of the