I'm a computer science master student, and I'm planning to graduate in spring 2022. In Finland, doctoral programs specifically state that applicants need to find a supervisor before applying. The supervisor has be be willing to mentor the applicant, and the research proposal, which is submitted with the application, also has be approved by the supervisor. I know that writing a decent research proposal takes a significant amount of time, which is why I have to get in touch with prospective supervisors well in advance. The question is when? My studies are approximately 30% completed, by the end of this academic year I will be done with everything except for my thesis. I don't have any solid idea about my future thesis yet. However, I have certain academic interests in machine learning and robotics.
Should I wait until I know the topic of my master's thesis next fall? Or should I start contacting doctoral programs next spring? The messy thing is that some universities have rolling admissions, while others have application periods once or twice a year. I have also been hopeful that by contacting professors at home university I could get to write a master's thesis connected to their research, would it be appropriate to ask them about such opportunities? I have taken several courses with some of them but I'm unsure they remember me since we normally have anywhere from 50 to 100 students in each course.