Geoscience Reference
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analytical or simulation/computational type that has not a relation to the subject
area for study; or
￿
mathematical equations describing the subject area.
￿
In the
firs case a model type can be one of the following:
self-organizing model (Ivachnenko et al. 1984);
￿
model of neural computation (Jordan and Sejnowski 2001; Obermayer and
Sejnowski 2001);
￿
genetic model (Neale and Cardon 1992); and
￿
graphical model (Koller and Friedman 2009).
￿
In the second case mathematical equations are formed depending on the subject
area that is considered. Selection of model type in many respects is no simple task.
Expert experience plays important role.
One of simple methods is method of self-organizing models that used effectively
for the problem solution of the spatial-temporal recovery of the data of monitoring.
The idea of this approach is based on traditional functions approximation theory.
Let an object or process be described by the model
ʨ
= f(a 1 ,
, n) where
parameters {a i }re
ect the quantitative, functional, and structural sections of the
phenomenon under study. A multitude of possible types of the function f is deter-
mined on basis of an expert estimation with consideration of a priori information and
heuristic set of partial descriptions of the phenomenon. The training sequence {fi} i }is
constructed which serves the basis for multi-row selection to choose the model of an
optimal complexity and acceptable accuracy. The
fl
first level of selection consists in
.
L ¼ C n ;
calculation of the row yi s }, where y i ¼ ga i 1 ;
ð
a i
Þ
s ¼ 1
; ...;
i ¼ 1
; ...;
n
The second level of selection gives the row {z p }, where z p ¼ gy j 1 ;
y j
C L ;
ð p ¼ 1
L Þ . The process of selection is continued till the most
regular mathematical description of the phenomenon under study is obtained. Esti-
mation of the accuracy of the obtained model and the choice of the moment of the end
of the process of selection depend on the chosen criterion of discrepancy between
theoretic and empirical image of phenomenon. The root mean square deviation cri-
terion is most often used, and polynomial serves as the function f. The procedure of the
models selection consists in a gradual complication of the polynomial approximation.
Method of the group consideration of arguments has been described in detail in
the work of Ivachnenko et al. (1984), where its various modi
; ...;
j ¼ 1
; ...;
cations are given with
examples of the ef
cient use in solving the applied problems.
Models of neural computation are usually applied for neuro-biological compu-
tation. For example, the Hodgkin
Huxley model, widely regarded as one of the
great achievements of 20th-century biophysics, describes how action potentials in
neurons are initiated and propagated in axons via voltage-gated ion channels. It is a
set of nonlinear ordinary differential equations that that approximates the electrical
characteristics of excitable cells such as neurons and cardiac myocytes. These
equations were introduced by Hodgkin and Huxley (1952) to explain the results
of voltage clamp experiments on the squid giant axon. Analytic solutions do not
exist, but
-
the Levenberg
-
Marquardt algorithm (Marquardt 1963), a modi
ed
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