Human life is not determined by mechanical fatalism or a single material factor;instead,based on the dualistic ontology and active force mechanism in the Unified Complex Systems Theory(UCST),it can be actively designe...Human life is not determined by mechanical fatalism or a single material factor;instead,based on the dualistic ontology and active force mechanism in the Unified Complex Systems Theory(UCST),it can be actively designed under the guidance of mind,in accordance with causal laws,and through systematic interactions.This study integrates the dualistic ontology of UCST,as well as the cooperative mechanism of active force(Fa)and passive force(Fp).Furthermore,by incorporating Master Jiqun’s philosophy of“life design”and the practical principle of“destiny establishment and transformation”from The Four Lessons of Liaofan Yuan,it constructs a three-dimensional framework for life design encompassing the dimensions of science,philosophy,and practice.The significance of this research lies in breaking through the predicament of materialism in the AI(artificial intelligence)era,explaining the autonomy and initiative of life,providing feasible pathways for life design,and ultimately achieving the in-depth integration of scientific rationality and the wisdom of traditional Eastern culture.展开更多
Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently...Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.展开更多
基金supported by the start-up funding from Westlake University under Grant Number 041030150118 and the scientific research project of Westlake University“Theoretical Research and Demonstration Application of Complex Systems and Deep-Sea Technology(Phase I)”under Grant Number WU2025A006.
文摘Human life is not determined by mechanical fatalism or a single material factor;instead,based on the dualistic ontology and active force mechanism in the Unified Complex Systems Theory(UCST),it can be actively designed under the guidance of mind,in accordance with causal laws,and through systematic interactions.This study integrates the dualistic ontology of UCST,as well as the cooperative mechanism of active force(Fa)and passive force(Fp).Furthermore,by incorporating Master Jiqun’s philosophy of“life design”and the practical principle of“destiny establishment and transformation”from The Four Lessons of Liaofan Yuan,it constructs a three-dimensional framework for life design encompassing the dimensions of science,philosophy,and practice.The significance of this research lies in breaking through the predicament of materialism in the AI(artificial intelligence)era,explaining the autonomy and initiative of life,providing feasible pathways for life design,and ultimately achieving the in-depth integration of scientific rationality and the wisdom of traditional Eastern culture.
基金Project supported by the National Natural Science Foundation of China(No.12402033)the National Natural Science Foundation for Distinguished Young Scholars of China(No.52225211)。
文摘Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.
