USACM-Student Chapter Seminar. Title: The Evolutional deep neural network for time dependent PDEs, Speaker: Yifan Du

USACM Student Chapter Monthly Seminar.

Thursday, March 27, at 4PM - 5PM (Eastern time - New York). 

Speaker: Yifan Du, Johns Hopkins University

Title: The Evolutional deep neural network for time dependent PDEs

ABSTRACT:  Evolutional deep neural networks (EDNN) provide an efficient framework for solving nonlinear partial differential equations (Du & Zaki, 2021). Training is only required to represent the initial condition, after which network parameters evolve in time using the governing equations, eliminating the need for further training. Boundary conditions are strictly enforced by the network design, and for Navier-Stokes equations, the divergence-free constraint ensures a solenoidal velocity field without requiring a pressure-projection step. EDNN’s compact architecture, which represents the solution in space and evolves in time, makes it memory-efficient and well-suited for forecasting nonlinear chaotic systems over long time horizons. Recent advances have further extended EDNN. The Multi-EDNN method decomposes a domain into elements and couples them via flux reconstruction, improving scalability. Additionally, nonlinear model order reduction and active learning techniques have enhanced EDNN’s efficiency in high-dimensional equations, broadening its applicability to complex and computationally demanding problems.

Bio: Dr. Yifan Du recently earned his Ph.D. in Mechanical Engineering from Johns Hopkins University and holds an M.S. in Mechanical Engineering from Purdue University. His research focuses on turbulence simulation, inverse problems, and scientific machine learning, with applications in flow physics and data assimilation. He has worked extensively with high-fidelity numerical simulations of high Reynolds number turbulent flows and developed novel computational methods that integrate physics-based modeling with data-driven approaches. Dr. Du has contributed to the development of machine learning techniques tailored for fluid dynamics. He formulated evolutional deep neural networks for solving time-dependent partial differential equations and designed physics-informed neural networks for reconstructing turbulent flows from sparse data. His work has been published in Physical Review E, Physical Review Fluids, and Journal of Computational Physics. He was awarded the Mark O. Robbins Prize in High-Performance Computing for his advancements in high-fidelity simulations and scientific machine learning.