PINNs and Deep Neural Operators for Building Digital Twins

Abstract: I will review physics-informed neural networks (PINNs) and summarize new extensions for applications in computational engineering. I will also review new representations of interpretable deep neural operators that take as inputs functions and distributions for system identification and real time inference. I will then present how we can interface PINNs and neural operators, such as DeepOnet. with finite elements for data assimilation, inverse problems and multiscale problems. Pretrained DeepOnets can serve as foundation models for building digital twins, and I will demonstrate such frameworks for problems in fluid and solid mechanics.

Presenter: George Em Karniadakis
The Charles Pitts Robinson and John Palmer Barstow Professor
of Applied Mathematics, Brown University;
Also @MIT & PNNL
https://sites.brown.edu/crunch-group/

Bio: George Karniadakis is from Crete. He is an elected member of the National Academy of Engineering, National Academy of Arts and Sciences, and a Vannevar Bush Faculty Fellow. 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 SES G.I. Taylor medal (2014), 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 153 (highest in Applied Mathematics and Fluid Mechanics) and he has been cited over 140,000 times.