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TAMIDS SciML Lab Seminar Series: Jia Zhao: Solving and Learning Phase Field Models Using Modified Physics Informed Neural Networks

September 8, 2021

3:00 pm - 4:00 pm

Online via Zoom

Meeting ID: 956 2165 2187

Passcode: SciML61492

Speaker: Jia Zhao, Ph.D.

Faculty Host: Ulisses Braga-Neto

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, we introduce some preliminary results on solving and learning phase field models using deep neural networks. In the first part, we 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, we 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. We will illustrate its approximation power by some interesting examples.

Biography: Dr. Jia Zhao received his Ph.D. in computational and applied mathematics from the University of South Carolina at Columbia back in 2015. Then he worked as a Postdoc at the University of North Carolina at Chapel Hill during 2015- 2017. He joined Utah State University as an Assistant Professor in 2017. His research focuses on computational modeling of complex multiphase fluids with applications in life science. His research projects have been funded by multiple resources, including NSF, NIH, NVIDIA, and S&P Global Ratings.