Hybrid CA Systems

Coupling Cellular Automata with Artificial Neural Nets

Christina Stoica

University of Duisburg

The nearly universal usability of cellular automata (CA) is well known. Famous examples for CA models are, for example, the modeling of processes of social differentiation (Schelling), the model of the biochemical hyper cycle (Boerlijst and Hogeweg), and the models of chemical waves (e.g., Gerhardt and Schuster). Such models become still more powerful by coupling CA with artificial neural nets (NN). Such CA-NN models may be called “hybrid systems” that contain certain characteristics of learning, adaptability, and flexibility. Two examples illustrate the advantages of hybrid neural CA.

The first example is a simulation of traffic flows. The cells of the CA represent types of cars, which are different with respect to velocity and type of driving. These artificial cars move on different lanes of a motor highway (“autobahnen”). Because of the different velocities and types of driving, accidents and other problems will occur that lead to backups. In particular, high density of traffic will increase the probability of accidents.

In order to regulate the traffic and to avoid too many accidents, the access roads to the highways are regulated by special traffic lights. These traffic lights stop the access if the density of traffic is too high and/or if there are already accidents resulting in backups. In the CA model the traffic lights are regulated by an artificial neural net, a so-called Kohonen feature map, which belongs to the type of unsupervised learning nets. The net is trained to certain critical values of traffic density. The practical use of such a system is the possible optimization of real regulating systems that already exist on the autobahnen in the German Rhein-Ruhr region.

The second example is a neural CA system that models individual learning processes in dependency of a certain social milieu. In this model the cells of the CA are not simply finite state automata but consist of several neural nets, that is hetero-associative networks and a Kohonen feature map. These networks are able to learn from other more advanced artificial learners in their (Moore) neighborhood, to construct concepts from perceptual data given to them by other cells and from the environment, to construct formation of analogies, and to generate semantical networks via the Kohonen feature map. The geometry of the CA represents the social structure of the environment; according to the differences of the individual learning processes, the CA geometry may change into the geometry of a Boolean network. First results indicate that “overeducated” social milieus, that is, milieus consisting of very educated “neighbors”, are often not favorable for individual learners because these (younger) learners are then only taking over already known facts and are not able to become creative in their own way.

Both examples demonstrate, in very different ways, how to use the power of hybrid neural CA systems.

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