Mathematical model(数学模型)

A mathematical model is an abstract model that uses mathematical language to describe the behavior of a system.

数学模型是一种使用数学语言描述系统行为的抽象模型。

Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.

数学模型的应用，不仅在自然科学和工程学科（如物理、生物、机电工程）而且在社会科学（如经济学、心理学、社会学和政治学）；物理学家、工程师、计算机科学家和经济学家使用数学模型最广泛。

Eykhoff (1974) defined a mathematical model as a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form.

Eykhoff (1974)把数学模型定义为一个现存（或准备建立的）系统的本质特征以实用的信息形式表达出来的一种描述。

Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models.

数学模型可以表现为多种形式，包括但不限于动态系统、统计模型、差分方程和博弈论模型。

These and other types of models can overlap, with a given model involving a variety of abstract structures.

一个指定的模型涉及各种抽象的结构，使得这些或者其他的模型存在交叉点。

There are six basic groups of variables: decision variables, input variables, state variables, exogenous variables, random variables, and output variables.

变量有六种基本形式：离散变量、输入变量、状态变量、外生变量、随机变量和输出变量。

Since there can be many variables of each type, the variables are generally represented by vectors.

每一个形式都会有许多的变量，所以用向量表示这些变量。

Mathematical modelling problems are often classified into black box or white box models, according to how much a prior information is available of the system.

根据系统已知初始信息的多少，数学建模问题经常被分成黑盒模型和白盒模型两种。

A black-box model is a system of which there is no a prior information available.

黑盒子模型用于表示初始信息未知的系统。

A white-box model (also called glass box or clear box) is a system where all necessary information is available.

白盒子模型（亦可称之为玻璃盒子或者透明盒子）用于表示所有必要信息已知的系统。

Practically all systems are somewhere between the black-box and white-box models, so this concept only works as an intuitive guide for approach.

实际上，所有的系统处于黑盒子模型和白盒子模型之间，所以这种方法只用于研究中的直观引导。

Usually it is preferable to use as much a prior information as possible to make the model more accurate.

常用的做法是使用尽可能多的初始信息让模型更准确。

 

 

via:https://www.sciencedaily.com/terms/mathematical_model.htm