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I'm not who you asked, but here's my current take:

Deep research maximizes uncertainty reduction (or information gain in other words). Uncertainty here could be model uncertainty if you are developing models, or a shift in the probability distribution for a particular question more generally. E.g., "Does P=NP?" would be an example of the latter.

It might be very general, applicable in many fields. Or it could be targeted at a particular field, but in a way which answers many questions.

Bayesian experimental design can do what I think is the easy part of the problem: maximizing information gained for a particular experimental problem statement. In my view, most of the time you can reasonably guess what Bayesian experimental design might tell you by looking at a state space of your exprimental data. So the math may not be strictly necessary. Unfortunately, not all research is experimental. And it won't tell you, for example, if you are missing a variable.

Framing the problem (which questions to ask, and how to answer them) seems like the most important part to me. Or at least it has been in my almost complete PhD.

These thoughts are in flux. I may have a different view in a year.

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