Proving you entered a marriage in good faith is based on many factors and lots of evidence. Living together is just a factor, but not the determining factor. If there is a good reason for you to be apart, especially in the interest of your marriage/life, then you submit proof of why you were apart and pursuing a PhD is a pretty darn good reason as far as I am concerned. This does not mean it will be a cake walk, it just means that you doing what you have to do for your career and to the benefit of your relationship does not necessarily reflect as negatively on your relationship as you might think. That may be a negative contributing factor, but the reason why might be a positive one and it is the totality of those circumstances that will determine. If you are at all concerned, please consult with an immigration attorney so you can get advice you can rely on. USCIS loves to fish out marriage fraud...even where it does not exist sometimes. It does not hurt to be prepared and it is well worth the money - much easier to prepare a good case than to fix one that has gone bad.
I don't think there is a perfect answer to your question. I think that ultimately the decision is yours. For filing purposes the bottom line is that if you continue to be a bona fide marriage (that happens to be temporarily separated solely for school purposes), then you may find yourself explaining that and providing all the proof of cohabitation, financial mingling, etc. that you may have. Consider that you will have to answer all questions truthfully and the form asks both your address and any other address in which you've lived since obtaining your CR card.
I strongly recommend that you hire an immigration attorney that's an AILA member from your area.
Good luck in all your pursuits.
The answer offered here is purely informational and does not create an attorney-client relationship. This answer is not to be construed as legal advice.
Be candid and forthright in your I-751 petition, and supply lots of documentation of your joint life together. You should explain the circumstances that cause you to have an additional residence (not in place of your joint residence) and include as much other joint financial, insurance, travel and other documentation as possible. It may be a good idea to have an attorney assist and advise.