CFDML21 Keynote: Discovering hidden fluid mechanics using PINNs and DeepONets

Presenter

George Em Karniadakis (GS h-index 111)
The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering, Brown University;
Also @MIT & PNNL

Abstract

We will present a new approach to develop a data-driven, learning-based framework for simulating fluid flows and for discovering hidden physics from noisy data. We will introduce 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 demonstrate the power of PINNs for several inverse problems, and we will demonstrate how we can use multi-fidelity modeling in monitoring ocean acidification levels in the Massachusetts Bay. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. We demonstrate that DeepONet can learn various explicit operators, e.g., integrals, Laplace transforms and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations; we will demonstrate the results of electroconvection and hypersonic boundary layers. More generally, DeepONet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously.

Bio

George Em Karniadakis George Karniadakis is from Crete. He received his S.M. and Ph.D. from Massachusetts Institute of Technology (1984/87). He was appointed Lecturer in the Department of Mechanical Engineering at MIT 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 continued to be a Visiting Professor and Senior Lecturer of Ocean/Mechanical Engineering at MIT. He is an AAAS 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 the SIAM/ACM Prize on Computational Science & Engineering (2021), the Alexander von Humboldt award in 2017, the SIAM Ralf E Kleinman award (2015), the J. Tinsley Oden Medal (2013), and the CFD award (2007) by the US Association in Computational Mechanics. His h-index is 111 and he has been cited over 58,000 times.