Physics-Constrained Learning Algorithms for Scientific and Engineering Problems Governed by Partial Differential Equations
Dr. Ming-Cheng Cheng
Professor of Electrical Engineering
Department of Electrical & Computer Engineering
Clarkson University, Potsdam, NY 13699, USA
Abstract: A physics-constrained learning simulation methodology based on proper orthogonal decomposition (POD) and Galerkin projection has been investigated for simulation of physical problems in several areas in engineering and science. Using this methodology, a physical problem of interest is projected onto a mathematical space constituted by a set of basis functions (or POD modes) that are trained by solution data collected from direct numerical simulations of the governing equation. The POD simulation model is then closed by the Galerkin projection of the governing equation onto the generated POD modes, which accounts for physical principles enforced by the governing equation and offers an accurate prediction beyond the training conditions. This is very different from most machine learning methods solving physical quantities, relying on statistical learning approaches to minimize the deviation of the prediction without enforcing physical principles. Such a learning approach often leads to a prediction inconsistent with the underline physical principles in case of extrapolation. The major drawback of the POD-Galerkin simulation methodology is its enormous computational effort needed to train a large structure if fine spatial resolution is needed. To overcome this issue, domain decomposition is applied to partition large structures into smaller standard building blocks. The trained building blocks can then be stored in a database and used for constructing larger structures. In this presentation, several physics-constrained learning algorithms derived from POD-Galerkin are introduced and applied to thermal analysis in CPUs/GPUs and simulations of quantum nanostructures and photonic crystals.
BIO: Ming-Cheng Cheng received the B.S. degree in Electrophysics from National Chiao-Tung University, Hsinchu, Taiwan, and the Ph.D. degree in Electrical Engineering from Polytechnic University, Brooklyn, NY. He is currently a professor in Electrical and Computer Engineering at Clarkson University, Potsdam, NY. His research has covered a wide range of areas including macroscopic and microscopic transport modeling of semiconductor devices, spin-polarized electron transport, electro-thermal simulations of devices and integrated circuits, electromagnetic simulation for core losses in magnetic materials, etc. Recently, he has devoted his effort to developing effective physics simulation methods and their applications based on physics-informed data-driven learning algorithms for different research areas, including dynamic thermal analysis of CPUs/GPUs/AI-chips, thermal-aware task scheduling in multi-core microprocessors, simulations of quantum nanostructures and electronic/photonic materials and devices, density-functional-theory (DFT) calculations, etc.
Thursday, January 23, 2025, 12:15-1:15 pm, CAMP 194
Join Link: https://clarkson.zoom.us/j/94088483647?pwd=2bmoDHPYozdIWgj1SrdVbqQaQUMUiz.1
*Co-Sponsored by IEEE student branch and HKN