現在有一種流行的方法，將數學模型分為機理模型和數據模型。我一直認為，對于工業應用來說，這種分類是不合適的。因為現實機械模型往往是兩者結合在一起的，只是程度的不同。

Now there is a popular method to divide mathematical model into mechanism model and data model. I always think that this classification is inappropriate for industrial applications. Because the real mechanical model is often combined with the two, but the degree is different.

所謂機理模型，本質上是理想模型(或抽象模型)。當模型能夠準確描述真實對象時(或誤差足夠小時)，模型的計算結果能夠與實際結果高度一致，使用起來非常方便。如果模型主要從事純算數或邏輯計算、幾何對象轉換等。，計算結果確實可以與現實高度融合。因此，在離散制造業中，3D設計模型可以大大提高R&D效率。

The so-called mechanism model is essentially an ideal model (or abstract model). When the model can accurately describe the real object (or the error is small enough), the calculated results of the model can be highly consistent with the actual results, so it is very convenient to use. If the model is mainly engaged in pure arithmetic or logical calculation, geometric object transformation, etc., The calculation results can be highly integrated with the reality. Therefore, 3D design model can greatly improve R & D efficiency in discrete manufacturing.

但是抽象模型總歸不等于現實對象。例如，歐幾里得幾何學中的線是沒有寬度的，而現實中的線是有寬度的。牛頓力學中的質點是沒有體積的，而現實世界中的優良物質是有體積的。

But the abstract model is not equal to the real object. For example, lines in Euclidean geometry have no width, while lines in reality have width. The particle in Newtonian mechanics has no volume, while the good material in the real world has volume.

實際工業對象是具體的。

The actual industrial object is concrete.

當理論模型應用于特定對象(如特定設備和工廠)時，問題就會出現：機理模型忽視的干擾，現實可能不容忽視；機理模型需要測量的參數，現實可能無法測量或無法測量。還有一個問題：當這些誤差太大而無法忽略時，該怎么辦？

When the theoretical model is applied to specific objects (such as specific equipment and factory), problems will arise: the interference ignored by the mechanism model may not be ignored in reality; The parameters of mechanism model need to be measured, which may not be measured or measured in reality. There is another question: what to do when these errors are too big to ignore?

解決方案大致有三種:1。充分考慮各種干擾。但這樣做，模型的復雜性會大大提高，不一定實用；2.準確測量相關參數。但是，這往往需要大量的成本，甚至影響實施效率，實用性差。3.更現實的方法是用實際數據糾正。因此，機制與數據模型相結合。事實上，第三種方法是平時常用的。

There are three solutions: 1. All kinds of interference should be fully considered. But in this way, the complexity of the model will be greatly improved, and it is not necessarily practical; 2. Accurate measurement of relevant parameters. However, this often requires a lot of cost, even affects the implementation efficiency, and the practicability is poor. 3. A more realistic method is to correct with actual data. Therefore, mechanism is combined with data model. In fact, the third method is usually used.

眾所周知，非線性物體通常可以局部簡化為線性模型。這是自然界中常見的現象。但是在工業場景中，除了局部使用的線性回歸模型之外，很少有純數據模型。因為用純數據模型建立非線性和時變模型時，往往難以保證可靠性，不適合工業應用。

It is well known that nonlinear objects can be reduced to linear models locally. This is a common phenomenon in nature. However, in industrial scenarios, there are few pure data models except for the local linear regression model. Because it is difficult to guarantee the reliability when using pure data model to build nonlinear and time-varying model, it is not suitable for industrial application.

因此，工業模型上實用的數學模型，往往是機制和數據的結合。

Therefore, the practical mathematical model of industrial model is often the combination of mechanism and data.

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