Analysis and Applied Mathematics Seminar
Jue Yan
Iowa State University
Cell-average-based fast Neural Network Method for time-dependent Problems
Abstract: In this talk, we present the newly developed cell-average-based neural network (CANN). The method is based on the integral or weak formulation of the partial differential equations and is motivated by finite volume schemes. A “stencil” concept is introduced, and the network structure is designed to align with the conventional one-step methods. The well-trained network parameters are identified as the scheme coefficients of an explicit one-step method. The CANN method is found to be relieved from the small time step CFL restriction. A large time step can be used to evolve the solution forward in time explicitly. The method is remarkably efficient and fast and processes unique properties. The method allows for sharp evolution of contact discontinuity and shocks with almost zero numerical diffusion. The method can be generalized to solve out-of-distribution initial value problems accurately. Toward the end of the talk, we will discuss an ongoing collaborative project with Aerospace Engineering. Experimental data from the lab is used to train the CANN method and simulate the evolution of thin film water flow for the run-back water multi-phase problem.
Monday November 13, 2023 at 4:00 PM in 636 SEO