"How to rigorously calibrate and validate the model?" What is wrong with the question? Can anyone guide me please?
"How to rigorously calibrate and validate the model?" sounds odd as a question because it lacks a subject and isn't a complete sentence. Usually, you only see "how to..." phrases directly following a verb (ex: "I know how to do that!", "He showed me how to do it.") or as the title of a how-to (ex: "How to Write a Check") (see https://en.wikipedia.org/wiki/How-to). It isn't a question; rather, it's more of a noun phrase. You could replace "how" with "the way" and it would still be grammatically correct, though it may sound funny to the listener depending on where you are and the context. Here is a way you could ask your question:
"How do you calibrate and validate the model?" "How do you calibrate and validate a model?" (in general) "How do I calibrate and validate the model?" "How do I calibrate and validate a model?" (in general)
If you want to add the adverb "rigorously", I recommend putting it at the end of the sentence: "How do you calibrate and validate the model rigorously?" This implies that you don't care about the other ways to calibrate and validate the model (because they aren't important or you already know them)--you want to know how to calibrate and validate it rigorously.
Also note if you say "the model", it refers to a specific model that the listener knows about. If you say "a model", it refers to any model in general.