Cross-cutting research of data- and model-driven methods by interlacing deductive and inductive cellular automata constructing method
| Project/Area Number |
16K13772
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyoto University (2017-2018)
Hokkaido University (2016) |
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Principal Investigator |
Nakano Naoto 京都大学, 国際高等教育院, 特定講師 (30612642)
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| Co-Investigator(Kenkyū-buntansha) |
宮路 智行 明治大学, 研究・知財戦略機構, 284326 (20613342)
川原田 茜 京都教育大学, 教育学部, 講師 (70710953)
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| Research Collaborator |
OBAYASHI Ippei
HIROSE Sanpei
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | セル・オートマトン / 応用数学 / 統計的モデリング / 偏微分方程式 / 数値解析 / データ主体解析 / データ駆動解析 / 数理モデル / データ解析 |
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| Outline of Final Research Achievements |
In this research, we studied empirical cellular automata (CA) construction method as a new modeling method for phenomena. We set the following two approaches to establish the empirical CA construction method: (A) numerical analysis on the selectivity of local rules of CA; (B) refinement of methodology for quantitative modelling. In (A), we investigated the relationship between solutions of CAs and PDEs by the use of interval operation and found the selection tendencies of resultant local rules of empirical CA mathematically. In (B), we constructed a model that mimics the solution behavior of nonlinear wave phenomena in a data driven manner. Furthermore, investigating the connection of our method with machine learning techniques and the method for analysis of global dynamics, we also obtained a novel method of modelling phenomenon.
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| Academic Significance and Societal Importance of the Research Achievements |
モデル駆動であるところの演繹的モデリングとデータ駆動であるところの帰納的モデリングを織り上げることで，統計的セル・オートマトン(CA)構成法を中心として状態の遷移の本質的な成分をデータから抽出する手法を構築した．これにより複雑な現象に対してもその遷移の骨子を捉えたモデリングが可能となり，さらには背後にある数学的な構造についての理解の深化が可能となった．本研究による手法によってさまざまな現象のメカニズムの理解に対して大いに助けとなる可能性がある．
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Report
(4 results)
Research Products
(13 results)
