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feynman1
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What's meant by 'affine' model in physical sciences? I guess it's related to some ideal or benchmark model?
affine transform has nothing to do with affine model?Baluncore said:A ideal model is compared with a real example.
The connection or mapping between the two is an 'affine transform'.
An affine transform preserves parallel lines.
I guess the model of the ideal could be called an 'affine model'.
https://en.wikipedia.org/wiki/Affine_transformation
There seems to be no such thing as an "affine model".feynman1 said:affine transform has nothing to do with affine model?
The term 'affine' refers to a mathematical model that represents a linear relationship between two or more variables. In this context, it is used to describe a model that assumes a proportional relationship between the variables being studied.
An affine model differs from other mathematical models, such as exponential or logarithmic models, in that it assumes a linear relationship between the variables being studied. This means that as one variable changes, the other variable changes in a constant and predictable manner.
An affine model can be used to describe a wide range of physical phenomena, such as the relationship between force and displacement in a spring, the relationship between temperature and volume in a gas, or the relationship between velocity and time in a moving object.
An affine model is commonly used in scientific research as a simplification of more complex relationships between variables. It allows scientists to make predictions and draw conclusions based on a linear relationship, which can be easier to analyze and interpret than other types of relationships.
While an affine model can be useful in many cases, it does have limitations. It assumes a constant and linear relationship between variables, which may not always accurately reflect real-world phenomena. It also cannot account for non-linear relationships or other factors that may affect the variables being studied.