I presented my work with Dr. Han at the applied Mathematics colloquium at Columbia University.
Abstract: This talk has two parts. In the first part, I will discuss the derivative-free loss method for solving PDEs and its analysis and applications to multiscale problems and perforated domains. The second part discusses a project related to learning in-between images. The new approach incorporates a PDE model in the latent space to assist the learning process. This approach shows robust results in capturing challenging dynamic, such as rotation and outflow, that cannot be captured by the current state-of-the-art method, optimal transportation. This is joint work with Jihun Han at Dartmouth.