The use of neural networks for approximation of nuclear data
- PDF / 1,136,594 Bytes
- 9 Pages / 612 x 792 pts (letter) Page_size
- 17 Downloads / 181 Views
EMATICAL SIMULATION IN NUCLEAR TECHNOLOGIES
The Use of Neural Networks for Approximation of Nuclear Data Yu. A. Korovin and A. V. Maksimushkina* National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe sh. 31, Moscow, 115409 Russia *email: [email protected] Received January 25, 2014
Abstract—The article discusses the possibility of using neural networks for approximation or reconstruction of data such as the reaction cross sections. The quality of the approximation using fitting criteria is also eval uated. The activity of materials under irradiation is calculated from data obtained using neural networks. Keywords: neural networks, calculation of the activity of irradiated materials, nuclear data, reaction cross sections. DOI: 10.1134/S1063778815120078
INTRODUCTION At present, for the analysis of various kinds of data, neural networks are being applied. They are widely accepted in fields such as medicine, economics, and physics. Neural networks are used mainly for solving of such problems as approximation and prediction. A neural network is a set of neurons that are con nected to each other in a certain way. Figure 1 repre sents the diagram of a neuron, where inputs are the output signals arriving at the input of the given neuron; Σ is the adder of input signals; f(x) is the calculator of the transfer function (the activation function); outputs are the output signals of the neuron; are the weight coefficients for input signals; Table 1 presents the most common activation func tion [1, 2]. The neural network can have both a singlelayer structure [2] (Fig. 2) and a multilayer structure (Fig. 3).
The matrix of weight coefficients of a singlelayer structure is of the form ⎡ϖ11 ϖ12 … ϖ1R ⎤ W = ⎢ϖ 21 ϖ 22 … ϖ 2R ⎥ , ⎢ ⎥ ⎣⎢ϖ S1 ϖ S 2 … ϖ SR ⎦⎥ where R is the number of elements of the vector of ini tial values and S is the number of neurons in the layer. In a multilayered structure [2] (Fig. 3), the output signals from some neurons are the input signals to other neurons. Neural networks are not linear and are very flexible in their structure, which allows them to be used in approximations and forecasting tasks, where there is a large amount of data or the data are poorly correlated with each other. Experimentally obtaining nuclearphysical data, for example, the reaction cross sections, is a techni cally and economically difficult task, so obtaining such data by calculations based on physical models describing complex processes taking place at interac bk
x1
ωk1
x2
ωk2
Activation function Σ
Inputs
xm
υk
ωkm Fig. 1. Diagram of a neuron.
1406
ϕ(x)
Outputs yk
THE USE OF NEURAL NETWORKS FOR APPROXIMATION OF NUCLEAR DATA
1407
Table 1. Activation function Name of function
Mathematical expression
Diagram x 1.5
⎧0 if x ≤ 0 ⎪ f (x) = ⎨1 if x ≥ 1 ⎪⎩ x else
Linear transfer function
1.0 f(x) −2
0.5 −1 −0.5
1
2
1
2
1
2
x 1.5 1.0
⎧1 if x ≥ T f ( x) = ⎨ ⎩0 else
Threshold transfer function
f(x) −2
σ(x) =
Sigmoid transfer function
0.5 −1 −0.5 x 1.5 1.
Data Loading...
