Title: Solving and learning phase field models using the modified Physics Informed Neural Networks
Abstract: In this talk, I will introduce some recent results on solving and learning phase field models using deep neural networks. In the first part, I will focus on using the deep neural network to design an automatic numerical solver for the Allen-Cahn and Cahn-Hilliard equations by proposing an adaptive physics informed neural network (PINN). In particular, we propose to embrace the adaptive idea in both space and time and introduce various sampling strategies, such that we are able to improve the efficiency and accuracy of the PINN on solving phase field equations. In the second part, I will introduce a new deep learning framework for discovering the phase field models from existing image data. The new framework embraces the approximation power of physics informed neural networks (PINN), and the computational efficiency of the pseudo-spectral methods, which we named pseudo-spectral PINN. In the end, I will illustrate its approximation power by some interesting examples.