Project Grant 2309778

The University of Missouri at Kansas City received a three-year, $156,046 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research into applying deep learning techniques to solve complex problems in science and engineering that involve partial differential equations. Specifically, the university will investigate how mathematical structures can inform the design of innovative deep neural networks to tackle challenging inverse problems in fields like electrical impedance tomography. Researchers will also examine the flexibility and mathematical properties of attention mechanisms in transformer architectures to potentially fuse these methods with applied mathematics approaches aligned with problem structures. The funding is intended to advance operator learning frameworks for mitigating ill-posedness in inverse problems and to train the next generation of computational mathematicians.