Automatic Derivation of Nonlinear State Equations by Using Artificial Intelligence in Inverse Problem of Complex Systems

复杂系统反问题中人工智能自动推导非线性状态方程

• 批准号: 13680449
• 负责人: OKAMOTO Masahiro
• 金额: $ 0.7万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13680449/
• 关键词: inverse problem; evolutional algorithm; complex system; genetic programming; inference system; nonlinear dynamics; automatic derivation system; generalized mass action law; 遺伝的アルゴリズム; 複雑系

Estimation of the interaction mechanisms among system components by using experimentally observed dynamic responses (time-courses) of some of the system components is generally referred to as "inverse problem". Especially in complex systems such as chaos, only a slight difference in interaction mechanism or in initial value of a system component causes a drastic change in time-course responses of system components.In this study, given experimentally observed time series data of system components, we have developed the inference system of interaction mechanism among system components based on evolutional algorithm (genetic programming, genetic algorithm). This system allows an automatic derivation of simultaneous differential equations based on generalized mass action law (GMA) which realize the experimentally observed time course data of system components. We have performed the validation of this sytem in the cases of two and three dimensional simultaneous nonlinear differential equations.

通过实验观察到的一些系统组件的动态响应（时间过程）的系统组件之间的相互作用机制的估计通常被称为“逆问题”。特别是在混沌等复杂系统中，系统元件的相互作用机理或初始值的微小变化，都会引起系统元件时程响应的剧烈变化，本文利用实验观测到的系统元件时间序列数据，开发了基于进化算法（遗传规划、遗传算法）的系统元件间相互作用机理的推理系统。该系统允许基于广义质量作用定律（GMA）的联立微分方程的自动推导，从而实现了系统组件的实验观测时间过程数据。我们已经在二维和三维非线性微分方程组的情况下进行了验证。

项目成果

Ueda, T., Koga, N., Ono, I., Okamoto, M.: "Application of Numerical Optimization Technique Based on Real-coded Genetic Algorithm to Inverse Problem in Biochemical Systems"Proc. of Genetic and Evolutionary Computation Conference (GECCO2002). 701 (2002)

Ueda, T.、Koga, N.、Ono, I.、Okamoto, M.：“基于实数编码遗传算法的数值优化技术在生化系统反问题中的应用”Proc。

山田晃範, 上田尚学, 岡本正宏: "逆問題のための重みつき評価関数を用いた進化アルゴリズムによる数値最適化 手法の設計・開発"第15回自律分散システムシンポジウム資料. 189-194 (2002)

Akinori Yamada、Naoaki Ueda、Masahiro Okamoto：“使用针对逆问题的加权评估函数的进化算法设计和开发数值优化方法”第 15 届自治分布式系统研讨会材料 189-194 (2002))。

Hirata, K., Maki, Y., Okamoto, M.: "Inference of a nonlinear network structure by evolutional algorithm"15th SICE Symposium on Decentralized Autonomous Systems. 195-198 (2002)

Hirata, K.、Maki, Y.、Okamoto, M.：“通过进化算法推断非线性网络结构”第 15 届 SICE 去中心化自治系统研讨会。

Okamoto, M.: "Inference of gene network based on S-system representation ("Bioprocess system engineering" pp. 41-52)"CMC-Publishers, Inc.. amount of page 309. (2002)

Okamoto, M.：“基于 S-系统表示的基因网络推断（“生物过程系统工程”第 41-52 页）”CMC-Publishers, Inc.. 第 309 页。（2002 年）

Ueda, T., Koga, N., Okamoto, M.: "Efficient numerical optimization technique based on real-coded genetic algorithm"Proc. of Intl. Workshop on Genome Informatics 2001. 451-453 (2001)

Ueda, T.、Koga, N.、Okamoto, M.：“基于实数编码遗传算法的高效数值优化技术”Proc。