Effective learning strategies based on principles like personalization, retrieval practice, and spaced repetition are often challenging to implement due to practical constraints. Here we explore the integration of AI tutors to complement learning programs in accordance with learning sciences. A semester-long study was conducted at UniDistance Suisse, where an AI tutor app was provided to psychology students taking a neuroscience course (N=51). After automatically generating microlearning questions from existing course materials using GPT-3, the AI tutor developed a dynamic neural-network model of each student's grasp of key concepts. This enabled the implementation of distributed retrieval practice, personalized to each student's individual level and abilities. The results indicate that students who actively engaged with the AI tutor achieved significantly higher grades. Moreover, active engagement led to an average improvement of up to 15 percentile points compared to a parallel course without AI tutor. Additionally, the grasp strongly correlated with the exam grade, thus validating the relevance of neural-network predictions. This research demonstrates the ability of personal AI tutors to model human learning processes and effectively enhance academic performance. By integrating AI tutors into their programs, educators can offer students personalized learning experiences grounded in the principles of learning sciences, thereby addressing the challenges associated with implementing effective learning strategies. These findings contribute to the growing body of knowledge on the transformative potential of AI in education.