大規模システムに関する科学的連立方程式モデルの発見

概要

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A novel and generic theory is formulated to characterize the structure of simultaneous equations. Based on the theory, an algorithm is developed to discover the structure of simultaneous equations governing an objective process through experiments, and the algorithm is implemented to the "Simultaneous Structure Finder(SSF)"program. SSF combined with another system SDS which discovers a quantitative formula of a complete equation derives a quantitative model of simultaneous equations reflecting scientfic laws underlying the objective process. The power of the proposed approach comes from the use of "minimal complete subsets" contained in any simultaneous equation set. They can be identified through controlled experiments on the objective process. This novel definition nicely characterizes the structure of simultaneous equations, and provides a measure to efficiently prune unnecessary search to identify simulaneous structure of an equation set. In this paper, the theoretical foundations of the structure identification and the algorithm of SSF are presented, and its efficiency and practicality are demonstrated and discussed with large scale working examples. Since the conventional equation discovery systems could not find such simultaneous equations in an efficient manner, this work is expected to provide a new research field on the scientific equation discovery.
2000-11-01