C. Nadir Kaplan
Virginia Polytechnic Institute and State University, Virginia, United States
Keywords: neural networks, nonconvex optimization, multiphysics
This project concerns the development of a fully automated, neural network based differential equation solver that not only finds the solutions but also the singularities of a physical system that carry physical information in its global behavior. To this end, we turn the task of differential equation solving into a nonconvex optimization problem and propose a novel algorithm that employs the local stability of the nonconvex landscape. As our ultimate goal, the solver has the potential to be generalized to a universal algorithm that determines all phase and stability properties of a physical system.