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I am learning the proposition, about, and on. I still need to improve my understanding. I wonder do I need to use about or on with the word information.

For example,

The method A can still give further information about the model.

The method A can still give further information on the model.

I feel on is awkward, however, I surprise why I cannot use of or for.

Which sentence is correct?

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It's difficult to say why some prepositions are used and others aren't. I think it just comes down to what people have settled on.

You're right that these aren't used:

information of the model
information for the model

However, both of these are fine:

information about the model
information on the model

But if you feel on is awkward, just use about.

There are some other words that could be used, but they either wouldn't be as common or they would be used in more specific contexts:

information regarding the model
information with respect to the model
information pertaining to the model
information relevant to the model


Note that in your example sentences, I would drop the and still. Also, both provide and more would be more natural words to use.

Putting all of that together:

Method A can provide more information about the model.

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