I'm currently in an REU program after finishing my freshman year of college majoring in Physics. My mentor is a graduate student, and I see him every day and we are working on an engineering project together. I see the lab's PI a couple times a week, and he is following my project, and occasionally has quite useful suggestions on how to proceed. He hasn't commented on my work, but he is aware of it, and probably occasionally discusses it with my mentor (a grad student). My work has certainly been satisfactory, but we most likely will not finish the project by the end of the summer, which was the original goal. This is not my fault, but I feel it will hurt my impression on the grad student and the PI. This Fall when I apply for other REU programs or internships for next summer, who should I ask for a letter of recommendation, if anyone at all? Is it reasonable to ask a grad student to write one, since I'll have worked under him for 2.5 months? Or should I go ahead and ask the PI, who has limited knowledge of my potential? I wouldn't ask either, due to the limited time frame for them to get to know me, but I'm afraid that mentioning research on an application without a supporting letter of recommendation could hurt me. Thoughts?