By the word science I understand it as a discipline of studying the physical world, or possible metaphysical world (like the mind) expressed in observable physics. Then by these objective observations, experiments, which must be repeatable, draw logical deductions and inferences. These in turn lead to more study, testing, conclusions until a body of knowledge and beliefs are developed which explain large portions of observed phenomena in the material world.
In what sense does Christian faith fall under this discipline? I would say in a few ways and sense.
First, in analyzing the scriptures and determining which translation is the most accurate of the original is according to a scientific discipline. This naturally brings our faith in some sense under science because the scriptures determine what our faith is.
Secondly, though to a much lesser extent the study of history, where texts outside of scripture are evaluated for trustworthiness by scientific comparison to other know facts of history, influences what many Christians believe. This historical science provides context for how many scriptures might be properly interpreted.
Third, in the same way that philosophy can follow rules about what is logical, what is a fallacy, etc. Christian theology based on its premises can is some sense become more disciplined and rigorous to ensure the thought patters or not illogical and that biblical texts and assumed beliefs are not developed under dishonest forms of reasoning. From this standpoint religious beliefs can spout from observed phenomena, such as for every good design, there is high probability that there is an architect or designer.
However, with all these aspects where Christian faith is influenced or in some sense brought under science, it is probably truer to say that it is brought under science only from the standpoint that it respects reason in whatever valid shape one might find it.
When turning to the scripture itself, science is considered, as a lower form of knowledge and biblical faith is a higher and more certain form of knowledge. In other words the knowledge that we can obtain from observing what is not seen, is greater than what we can achieve from what is seen:
Now faith is the assurance of things hoped for, the conviction of things not seen. (Hebrews 11:1)
The scripture treats knowledge that comes from God through the Bible as a light. It means this in a literal sense, whereby the knowledge we might obtain by light, or the sight which we can obtain, is not possible but by faith. Therefore to simply things, the Bible describes a scientist without faith as more or less a man who is literally blind to higher forms of knowledge. He can see the physical world but not the spiritual. No matter how hard he tries to ‘see’ he can’t because he has no ‘light’.
Naturally the result is that such a blind mind concludes the gospel is just foolishness because he can’t see it:
The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned. (1 Corinthians 2:14)
The Greek root of the word ‘discerned’ means to investigate, or appraise. In this sense those without faith are not able to judge, evaluate, or discern the meaning of what is certain and true about God because it seems foolish from beginning to end, having no light which alone comes from faith in the gospel.
Conclusion: There are aspects where Christian faith is under science, these occur where physical and logical elements overlap or influence Christian thinking. Christian faith by nature puts itself above reason and science, and what can be seen with the eye altogether, for it fixes itself upon God, who is above all things whatsoever.