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The perceptron structure, on the basis of which the database is built,
is defined by a number of the input and output parameters and
a required accuracy.
The number of input neurons corresponds to the number of parameters
defining of the cluster properties:
.
The output perceptron data are the expansion coefficients of the
scattering matrix elements in series of the generalized spherical functions.
The data for perceptron training was obtained using Mackowsky & Mishchenko
code [34].
At the number of nonzero coefficients was equal to approximately 2224.
So, the number of output neurons was 30, and the number of "hidden" layers
was 2 with 30 neurons in each layer.
The generation algorithm for a fractallike cluster of particles can be
defined as follows:

(1) 
where is the gyration radius of the cluster

(2) 
and is the distance from the th particle to the center of mass
of the cluster.
Typical cluster structures with the same , and but
produced under different initial generation conditions
are presented in Fig.1.
Figure 1:
Typical clusters formed of 10 and 20 subparticles.

Up to now, about two hundred points for the input parameters in the range of
,
, and for
, , and were utilized for
training the perceptron.
As the cluster structure depends on the generation conditions
the expansion coefficients were averaged over 57 realizations of
the clusters (for N < 35).
During this training process the perceptron was defining and
memorizing a hypersurface in space of inputoutput parameters
that in the best way corresponded to the data set presented for training.
The trained perceptron allows calculating the approximate values of
the expansion coefficients for any input data from the data range
that was used for the training.
Figure 2:
Dependency of the and
coefficients on . is the coefficient number.

Some examples of calculation of the dependencies of expansion coefficients
and of the scattering matrixes elements and
are given in Fig.2.
The points correspond to the data obtained directly from the theory of
light scattering by a cluster of spherical subparticles.
Solid curves show data calculated by the perceptron.
Figure 3:
Linear polarization
degree vs the scattering angle .
Solid curve corresponds to the actual values,
dotted line shows the values calculated by the perceptron.

In Fig.3 the linear polarization degrees of light scattered by clusters is
presented. Note, that this refractive index
(; ) was not used in perceptron training,
which illustrates the potential of our database.
Advantages of the database are its small volume and quick access to the data.
Moreover, there is a possibility to extend and make the database more precise
without an increase of data time access and the volume of the database.
This research was supported by INTAS grant N 199900652.
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