|InterJournal Complex Systems, 1820
|Manuscript Number: |
Submission Date: 2006
|Data-driven technique to model complex systems|
We analyze the limitations of the traditional computational approach and discuss an alternative approach which focuses (1) directly on data and their dependencies, and (2) computational techniques to automate the data generalization and model building process. Usually, this gets done by a scientist during a data analysis and model building process. First, we compare classical program-driven computing model with a weak environment interaction and computing model driven by events/data in the environment. The program-driven model usually gets designed and built by a programmer, and this is a challenge for complex models. The environment, modeled by input-output operations, has a limited impact on the program which is driven by its internal hand-built program logic. We discuss then a computing model driven by data and data dependencies connected (associated) in a data pair. The dependencies include, in particular, the initial and boundary conditions as well as any other applicable data context. We indicate that the environmental dynamics may drive and shape the computational model by using the memory-based mechanisms of handling data pairs. Focus on data taken in its context (data pair) stresses the primary role of dependencies vs. computing, and indicate that for complex systems the classical computing paradigm is limited. So, we discuss reasoning based on data and their dependencies as a preferable method for problem solving in complex systems. To build a model, that is, to find the common features, the data pairs get generalized and reinforced building a problem-specific memory structure. This memory structure becomes a model, a data-based reasoning engine that represents the data-based (data-encoded) knowledge about the specific application domain. The reasoning then gets performed as a search in that memory structure. Such a model does not depend on complexity of dedicated problem-solving algorithms, and instead introduces a memory structured by data/dependencies (data pairs). To find the common features, if any, the data pairs get generalized computationally, using, for example, spatial superimposition or neural network techniques. Then a search in that memory structure using a new data generates a new context, that is, the dependency to be looked for. This alternative data-driven model encodes the knowledge as data and their dependencies - associations or data pairs. In traditional models, the knowledge gets encoded incrementally, for each elementary volume, by relationships between input and output flows and the “forces” driving the change. So, it requires then the incremental build-up the solution, a formidable task for complex problems. So, for complex systems, the data-driven reasoning model may become the primary method of problem-solving, since traditional symbolic models and related computational methods turn out to be intractable. In addition, the massively-parallel search in structured memory is a promising technology that can be effectively implemented in the state-of-the-art advanced silicon architectures such as field programmable gate arrays (FPGAs), associative memory arrays, and in the advanced 3D optical systems. To model the data-driven memory structuring, we introduce a natural way to build the representing memory structure by compression the data stream using the space-division multiplexing of the data pairs. That mechanism compresses the input data stream into the novelty-encoded space-multiplexed memory structure. In the highly-stable environments, the resulting architecture has a dense core and the novelty rings, and has some similarities with the genetic dynamics of cellular systems in evolutionary timeline. Such an encoding mechanism creates the multi-scale hierarchical structure with the various scales due to the novelty elements in the environmental data. The prototype of the data-driven model-building environment has been built to demonstrate feasibility of the proposed technique. Its design concepts are presented and discussed. The neural networks techniques are used for data pairs generalization. The examples of ballistic problem and inverted pendulum stabilization problem are presented and discussed as well as spectra interpretation problem.
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