# 什么是模型？

最近在上人工智能课程，总看到模型model一词。加之一月份又要参加2019年的数学建模美赛，所以对「模型」这个概念感到很好奇。和『大佬』这些词一样，都是上大学后才了解到的。

关于模型，摘抄原文如下：

A model can come in many shapes, sizes, and styles. It is important to emphasize that a model is not the real world but merely a human construct to help us better understand real world systems. In general all models have an information input, an information processor, and an output of expected results. Modeling Methodology for Physics Teachers (more info) (1998) provides an outline of generic model structure that is useful for geoscience instruction. In “Modeling the Environment” Andrew Ford gives a philosophical discussion of what models are and why they are useful. The first few paragraphs of Chapter 1 of Ford’s book are worth a look.

Key features in common with the development of any model is that:

- simplifying assumptions must be made;
- boundary conditions or initial conditions must be identified;
- the range of applicability of the model should be understood.

概括地来说，模型首先不局限于形式，有很多表达方式。它用来抽象现实世界的某一个方面。

模型有输入，处理机制和输出。我们要优化我们的处理机制以便让由输入得到的输出符合我们的期待。

有接触到的比如数模里的函数，AI课学习的「决策树」『minimax』等，模型有很多不同的表达形式。或许使用最多的还是函数。

# 模型类型举例

## Conceptual Models

Conceptual Models are qualitative models that help highlight important connections in real world systems and processes. They are used as a first step in the development of more complex models.

## Interactive Lecture Demonstrations

Interactive Lecture Demonstrations Interactive demonstrations are physical models of systems that can be easily observed and manipulated and which have characteristics similar to key features of more complex systems in the real world. These models can help bridge the gap between conceptual models and models of more complex real world systems.

## Mathematical and Statistical Models

Mathematical and Statistical Models involve solving relevant equation(s) of a system or characterizing a system based upon its statisical parameters such as mean, mode, variance or regression coefficients. Mathematical models include Analytical models and Numerical Models. Statistical models are useful in helping identify patterns and underlying relationships between data sets.

## Teaching with Visualizations

Teaching with Visualizations By this we mean anything that can help one visualize how a system works. A visualization model can be a direct link between data and some graphic or image output or can be linked in series with some other type of model so to convert its output into a visually useful format. Examples include 1-, 2-, and 3-D graphics packages, map overlays, animations, image manipulation and image analysis.

## 总结

- 抽象或许是建模的第一要素
- 模型概念很广
- AI所说的“我们训练了一个很好的模型”指的就是利用我们的模型，输入所给的输入，得到的输出很符合我们的期望。比如给机器人一张视觉的影像，他知道该怎么移动怎么操作，知道拿起苹果放到指定位置，这符合我们对输出的期望（输出就是机器人所做出的动作）。这就是好的模型。