2023 Fiscal Year Final Research Report
Method for extracting conserved quantities of black box differential equation models and its application to network analysis
| Project/Area Number |
20K11693
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60020:Mathematical informatics-related
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| Research Institution | Kobe University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | 保存則抽出手法 / ブラックボックスモデル / 深層学習 / 社会ネットワーク解析 |
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| Outline of Final Research Achievements |
In recent years, black-box differential equation models such as neural ordinary differential equations have been attracting much attention. Because such models do not admit symbolic representations, it is difficult to investigate their properties, including the existence of conservation laws.
In this study we constructed a data-driven method that finds conserved quantities for black-box differential equation models. More precisely, conserved quantities are modeled by neural networks, and the neural networks representing the conserved quantity are trained so that the model accuracy is improved when the black-box model is modified so that this quantity is conserved. We numerically confirmed that conservation laws can be certainly extracted from various differential equation models using this method. We developed a statistical method for the analysis of structural changes in networks.
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| Free Research Field |
数値解析，深層学習，数理モデリング
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| Academic Significance and Societal Importance of the Research Achievements |
開発した手法は，未知の保存量を抽出するだけでなく，発見した保存則を解析対象のブラックボックスモデルに追加することができる．従って，既存の数理モデルや，シミュレーションプログラムに対して，この方法を適用すると，未知の保存則を発見し，それを保存するようにモデルやシミュレーション結果を修正することができる．これは，モデルやシミュレーションプログラムの予測精度を向上させる効果をもつと期待され，既存のシミュレーションソフトウェアなどを改良することができる可能性をもつ．
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