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Urban Cellular Automata: The Inverse Problem
Giovanni A. Rabino and Alessandra Laghi
Politecnico di Milano
Dipartimento di Architettura e Pianificazione
Piazza Leonardo da Vinci 32, Milan, I-20133 Italy
giovanni.rabino@polimi.it
alessandra.laghi@libero.it
Abstract.
The issues regarding complex systems and the validation of their
models has recently come on the fore; as Cellular Automata do belong to this
category, they are directly involved in this revision. A major issue arising from
the debate regards the procedure adopted to test models of these systems:
application of a priori ipotheses to one case study. This kind of procedure is
seen as unreliable, and as a generator of misleading models, whose predictions
do not have solid foundations. Analyzing the problem in a general perspective,
it (that is, the choice of the family of models to use) could be formulated as an
inverse problem, based on an inductive method, which tries to formulate rules
gaining information from data and doing the least number of a priori ipotheses.
1.
Introduction
The problem of validating models of complex systems (namely, Cellular Automata)
has recently arisen in geography, pointed out in a paper by M. Batty and P. Torrens
[1]. In this paper it was highlighted the difficulty of validating such kind of model
simply running it to reproduce the dynamics of one case study. The main issue against
this procedure is the complexity of the system itself, which makes very difficult test
the hypotheses made a priori in structuring the model; as a consequence, simulations
and predictions are not sufficiently reliable. Since the complexity of cities is a matter
of fact, the problem right now is try to find a new approach to model them, in order to
prevent the application of this kind of models only for “story telling” purposes.
This paper presents the problem of modeling land use dynamics using Cellular
Automata (CA from this point forward), particularly focusing on the creation of
transition rules. A new approach is used: the creation of rules starts from data analysis
instead of a priori hypotheses, and the perspective is inductive instead of deductive.
The second section of this paper develops the general issue of inverse problem,
while the third relates it to urban CA. The fourth section presents the available data,
the operational problems arisen and their solutions and the first results. Finally, the
fifth section is for conclusions and suggestions for further research.
S. Bandini, B. Chopard, and M. Tomassini (Eds.): ACRI 2002, LNCS 2493, pp. 349-356, 2002.
