Professor Barr's research involves (1) mathematical simulation methods for computer graphics (2) developing new types of mathematical and computational methods for the study of biophysical behaviors and structures, and (3) technological leveraging for medical health care and new medical devices, including new physics-inspired machine learning algorithms to enhance the state of the art in MRI Imaging. In addition, he has been collaborating with JPL researcher Dr. Martin Lo on new computational and mathematical methods for utilizing the InterPlanetary Superhighway for developing new missions in the Solar System. All of these research areas involve the development and application of new mathematical and computational methods in the context of new applications in the physical sciences.