"Physics-Informed Learning Machines for Physical Systems"
In this talk, we will present a new approach to develop a data-driven, learning-based framework for predicting outcomes of physical systems and for discovering hidden physics from noisy data.
A key concept is the seamless fusion and integration of data of variable fidelity into the predictive models. First, we will present a Bayesian approach using Gaussian Process Regression (GPR), and subsequently a deep learning approach based on neural networks (NNs) and generative adversarial networks (GANs). Unlike other approaches that rely on big data, here we “learn” from small data by exploiting the information provided by the physical conservation laws, which are used to obtain informative priors or regularize the neural networks. We will also make connections between GPR and NNs and discuss the new powerful concept of meta-learning. We will demonstrate the power of PhILMs for several inverse problems in fluid mechanics, including wake flows and shock tube problems, where traditional methods fail due to lack of boundary and initial conditions.
Karniadakis received his S.M. and Ph.D. from Massachusetts Institute of Technology. He was appointed Lecturer in the Department of Mechanical Engineering at MIT in 1987 and subsequently he joined the Center for Turbulence Research at Stanford / Nasa Ames. He joined Princeton University as Assistant Professor in the Department of Mechanical and Aerospace Engineering and as Associate Faculty in the Program of Applied and Computational Mathematics. He was a Visiting Professor at Caltech in 1993 in the Aeronautics Department and joined Brown University as Associate Professor of Applied Mathematics in the Center for Fluid Mechanics in 1994. After becoming a full professor in 1996, he continues to be a Visiting Professor and Senior Lecturer of Ocean/Mechanical Engineering at MIT. He is an AAS Fellow (2018-), Fellow of the Society for Industrial and Applied Mathematics (SIAM, 2010-), Fellow of the American Physical Society (APS, 2004-), Fellow of the American Society of Mechanical Engineers (ASME, 2003-) and Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA, 2006-). He received Alexander von Humboldt award in 2017, the Ralf E Kleinman award from SIAM (2015), the J. Tinsley Oden Medal (2013), and the CFD award (2007) by the US Association in Computational Mechanics. His h-index is 89 and he has been cited over 40,000 times.
Dr. George Em Karniadakis
Division of Applied Mathematics
Brown University & Department of Mechanical Engineering, MIT