Zoom link: https://wayne-edu.zoom.us/j/99751642454?pwd=cjZIM1FUU0lEdUIweHpMRTBxYmd2QT09

Title: Data-driven optimal control with neural network modeling of gradient flows

Abstract: Extracting physical laws from observation data is a central challenge in many diverse areas of science and engineering. We propose Optimal Control Neural Networks (OCN) to learn the laws of vector fields in dynamical systems, with no assumption on their analytical form, given data consisting of sampled trajectories. The OCN estimator consists of a neural network representation, trained with an optimal control solver. We provide error bounds for both the solution and the vector field, and the bounds are shown to depend on both the training error and the time steps between sampled data. We also demonstrate the effectiveness of OCN, as well as its generalization ability, by testing on several canonical systems, including the chaotic Lorenz system.  Time permitting, I will also discuss some recent advances on a novel training method: Adaptive Gradient with Energy.  

Bio Info:  Hailiang Liu is an applied mathematician with expertise in nonlinear partial differential equations and numerical analysis. He also works on the mathematical theory of deep learning and data-driven modeling.  Liu completed all his degrees in Mathematics, with Master degree from Tsinghua University, and PhD degree from Chinese Academy of Sciences. He was an Alexander von Humboldt fellow in Germany from 1997-1999, an assistant professor at UCLA from 1999-2002.  Liu moved to ISU as an associate professor in 2002, then up to full professor in 2007. He was appointed professor of Computer Science in 2020,  in addition to his primary position in the Mathematics Department.  He is a core member of the Translational AI Center (TrAC) at ISU since 2021. Liu’s honors include the Humboldt Research Fellowship in 1997, the Holl Chair in Applied Mathematics from 2002-2012, the LAS Award for Outstanding Achievement in Research in 2019.  He has published more than 160 research papers, mostly in Numerical Analysis and Applied Partial Differential Equations.