Applied Math Seminar-Solving and learning phase field models using the modified Physics Informed Neural Networks
Fri, 25 September, 2020
6:00pm
Yanxiang Zhao is inviting you to a scheduled Zoom meeting.
Topic: Applied Math Seminar
Time: Sep 25, 2020 02:00 PM /Eastern Time (US and Canada)
Title: Solving and learning phase field models using the modified Physics Informed Neural Networks
Jia Zhao, Assistant Professor of Mathematics, Utah State University
Email: [email protected]
Abstract: Phase field models, including the Allen-Cahn type and Cahn-Hilliard type equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, efficient, and stable numerical algorithms for solving the phase field models has been an active field for decades. In the meanwhile, developing reliable and physically consistent phase field models for applications in science and engineering have also been intensively investigated.
In this talk, I will introduce some preliminary 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 or SPINN. In the end, I will illustrate its approximation power by some interesting examples.
Join Zoom Meeting
https://gwu-edu.zoom.us/j/96683619015?pwd=VU1rTTJHUit6bVNYc0pZbUY0T1VtQ…
Meeting ID: 966 8361 9015
Passcode: 098871