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unsupervised learning. Concerning supervised learning the aim is to train a network which
should express a specific function [83]. One does have a
set of data pairs which are
combinations of inputs and targets values. More details on supervised learning can be
found in literature [84-87]. In contrast to supervised learning
there is the unsupervised
learning. In this form of learning one has a set of values and a cost function that has to be
minimized. The main areas which are targeted by this kind of learning are: estimation
problems,
clustering application, the estimation of statistical distributions,
filtering and
data compression. More details on unsupervised learning can be found in literature [85,
88, 89].
There is another type of artificial neural networks proposed by Chua
et al
and
called
cellular neural network (CNN). CNN is a combination of cellular automata and traditional
artificial neural networks [90-92]. CNN consists of huge number of cells which are
connected locally, that is, each cell is only connected to its neighbors. CNN is getting very
popular in image processing [93]. One can train it by heuristic
learning methods such as
genetic algorithms and iterative annealing [94]. Another way to train the CNN is direct
mapping of equation on the CNN. If we have PDE with two
or more independent variable, it
is possible to convert it to set of ODEs with one independent variable. We know that CNN is
consisting of many integrators and some other active and
passive elements which are
coupled together with a specific topology. These coupled integrators are helpful for solving
ODEs. Hence, if we solve these sets of ODE on a single CNN layer, the solution of complete
system is solution of our PDE.
