MINDS Seminar on Machine Learning

Title : Collaboration between PDEs and machine learning: solving PDEs and learning dynamical systems using neural networks

Speaker : Jihun Han (Dartmouth College)

Abstract : This talk has two main parts. Firstly, I will discuss a stochastic approach for solving PDEs: the derivative-free loss method (DFLM). I will cover its analysis and highlight its advantages in addressing multiscale problems and perforated domain problems in a non-intrusive manner. In the second part, I will introduce a method for learning in-between imagery dynamics. This method involves integrating PDE models within the latent spaces to enhance learning. Notably, this method exhibits robustness in capturing intricate dynamics, such as rotation and outflow, which are challenging for existing state-of-the-art methods of optimal transport.