Reduction of the degreess of freedom of dynamical systems by machine learning
| Project/Area Number |
18K03469
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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 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Toho University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2020: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 機械学習 / 非平衡ダイナミクス / 縮約理論 / 相転移ダイナミクス / 非平衡動力学 |
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| Outline of Final Research Achievements |
In this project, we developed a general framework supported by machine learning to derive closed time-evolution rules for a small number of macroscopic variables, such as internal energy, from the time-evolution rules for a system with large degrees of freedom, such as condensed matter, which has been done by the intuition of researchers in most cases. We examined its usefulness by applying the method to the system with discrete variables such as cellular automata and spin systems (Potts model). These yields a plausible result, e. g., about the relationship between the symmetry of the initial conditions and the minimum degrees of freedom to constitute a closed dynamical system.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究が対象とするのは、大きな自由度を持つ複雑な系を人間が理解するために不可欠な次元（情報）の削減である。これはあらゆる科学にまたがる極めて普遍的な営みであると言える。統計物理学は特にこれを主たる目的としてきた学問分野であるが、ほとんどの場合には研究者の直観にたよった大胆な近似を行うのが常道であり、近似の妥当性を確立されたミクロなモデルから正当化できることは稀である。本研究では近年発展の著しい機械学習の助けによってデータに基づく根拠を持った縮約モデル（現象論）を構築する新しい方法を提示し、具体的な適用例によって有用性を示した。
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Report
(6 results)
Research Products
(7 results)
