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第501行： − 复杂系统的数学模型有三种类型: 黑箱(现象学)、白箱(基于第一性原理的机制)和灰箱(现象学与机制模型的混合)。 卡尔米科夫列夫 v，卡尔米科夫维切斯拉夫解决方案+ 第663行：
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→Complex systems modeling
===Complex systems modeling===
===Complex systems modeling===
===Complex systems modeling===
===Complex systems modeling复杂系统建模===
复杂的系统建模
复杂的系统建模
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. Solution">
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. Solution">
复杂系统的数学模型分为三种：黑匣子（现象学），白匣子（力学，基于第一原理）和灰匣子（现象学和力学模型的混合）。在黑匣子模型中，基于个体的复杂动态系统机制仍然是个谜。
{{Citation
{{Citation
}}</ref> In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.
}}</ref> In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.
} / ref 在黑盒模型中，复杂动态系统中基于个体的(机制)机制仍然是隐藏的。复杂系统的数学模型黑箱模型是完全非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们不能研究这样一个非透明模型的子系统之间的相互作用。复杂动态系统的白盒子模型具有“透明墙” ，直接揭示了内在机制。一个动态系统的微观、中观和宏观层面的所有事件在其白盒模型演化的所有阶段都是直接可见的。在大多数情况下，数学模型使用沉重的黑箱数学方法，不能产生复杂动态系统的机械模型。灰盒模型是中间的，结合了黑盒和白盒方法。单种群增长的逻辑确定性个体元胞自动机模型复杂系统的白盒模型的产生与建模主体先验基础知识的必要性问题有关。确定性逻辑元胞自动机是白盒模型存在的必要条件，但不是充分条件。白盒模型的第二个必要前提是被研究对象的物理本体的存在。白盒建模代表了基于第一原则的自动超逻辑推理，因为它完全基于主体的确定性逻辑和公理系统。白盒建模的目的是从基本公理推导出关于被研究对象的动力学的更详细、更具体的机械知识。在创建其白盒模型之前，必须确定主体的内在公理系统，这使得白盒模型区别于基于任意逻辑规则的细胞自动机模型。如果细胞自动机规则没有从主题的第一原则制定，那么这样的模型可能有一个弱相关性的实际问题。
} / ref
黑匣子模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白匣子模型是透明的，直接显示了潜在的机制。在动态系统白匣子模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑匣子方法，这些方法无法生成复杂动态系统的机械模型。灰匣子模型是中间模型，结合了黑匣子方法和白匣子方法。
复杂系统白匣子模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白匣子模型的必要条件，但不是充分条件。白匣子模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白匣子建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白匣子建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白匣子模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白匣子类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型
==Hardware-based ("hard")==
==Hardware-based ("hard")==