Project Grant 2205627

This five-year $550,000 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research at Carnegie Mellon University on variational methods for materials and imaging. The University will pursue a mathematically rigorous understanding of emerging nonlinear phenomena across physical and technological applications, from analyzing instabilities in materials science to image analysis in computer vision. Researchers will develop innovative mathematical tools to address higher-order derivatives, discontinuous fields, multiscale interactions, and competing bulk and surface energies that prevent application of established theories. This foundational work will provide analytical and machine learning-based approaches to materials defects, epitaxy, magnetics, composites, image denoising, edge detection, segmentation and registration. Training opportunities will also be provided to next-generation leaders in applied analysis at the intersection of mathematics, computing, engineering and physical sciences.