George Em Karniadakis

 George Em Karniadakis (h-index 118)


"People who wish to analyze nature without using mathematics must settle for a reduced understanding." Richard Feynman 

Full CV

Karniadakis elected to the National Academy of Engineering (class 2022)

The Charles Pitts Robinson and John Palmer Barstow 
Professor of Applied Mathematics and Engineering,
Research Scientist, Massachusetts Institute of Technology 
Room 312,  170 Hope Street
Phone: +1 401 863 1217 
[email protected] 

Ph.D., Massachusetts Institute of Technology, 1987



Introduction to Computational Linear Algebra 


Numerical Solution of Partial Differential Equations I

APMA 2560

Numerical Solution of Partial Differential Equations II


Multiscale Computational Fluid Dynamics


George Karniadakis received his S.M. (1984) and Ph.D. (1987) 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 (1993) in the Aeronautics Department. He joined Brown University as Associate Professor of Applied Mathematics in the Center for Fluid Mechanics on January 1, 1994. He became a full professor on July 1, 1996.  He has been a Visiting Professor and Senior Lecturer of Ocean/Mechanical Engineering at MIT since September 1, 2000. He was Visiting Professor at Peking University (Fall 2007 & 2013). He has a joing appointment with PNNL since 2013. He is a 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 CSE/ACM prize (2021), the SIAM Ralf E Kleinman award (2015), the (inaugural) J. Tinsley Oden Medal (2013), and the CFD award (2007) by the US Association in Computational Mechanics.  His h-index is 118 and he has been cited over 62,500 times (see his google scholar citations).  You can also check out his Geneaology Tree (remember to zoom in!). Here is his wikepedia profile

Research Interests

His current research interests are on machine learning for scientific computing (Scientific Machine Learning), that is how to solve and discover new PDEs via deep learning, hence removing the tyranny of grids and using gappy data only. Check here to find how to use deep neural networks to solve the Schrodinger equations with only 10 lines of Tensorflow code!  Check here to see how to use deep CNN to classify different types of red blood cells in sickle cell anemia.

His broad research interests focus on stochastic multiscale mathematics and modeling of physical and biological systems.  Current thrusts include probabilistic numerics, stochastic simulation (in the context of uncertainty quantification and beyond), fractional PDEs, and multiscale modeling of complex systems (e.g., the brain). Can you believe that we solve problems in 100 dimensions - check this out! Read here about our work on sickle cell anemia and also on modeling malaria from first principles, which was also featured on the web site of the National Public Radio. Read also about our work on the first large multiscale modeling of a brain aneurysm (finalist in the Gordon Bell Award, Supercomputing'11). Our new area is neurovascular coupling in the brain, i.e., bridging the gap between neuroscience and vascular mechanics. New experimental evidence suggests the intriguing possibility that by slightly modulating the brain blood flow one can control information processing -- read our paper here! Recent feature article of our work ("Blood in Motion") in American Scientist.  Particular aspects include:

Fractional PDEs: A breakthrough paper!

Numerical solution of stochastic differential equations: SISC article, also PNAS article

Modeling uncertainty with polynomial chaos: PNAS article, CiSEJCP

Biophysics - Multiscale modeling of biological systems: PNAS (sickle cell anemia); PNAS (blood viscosity)PNAS (malaria) articlePNAS (thrombosis) articlePRS article

Atomistic/Mesoscopic modeling - Dissipative Particle Dynamics: JCP (triple-decker)PRL (adaptive BCs)

Low Dimensional Modeling - Gappy Data - Data assimilation: JCP article 

Spectral/hp Element and Discontinuous Galerkin methods:  OUP Book

Turbulent Drag Reduction: Science article

DNS/LES of turbulence in complex geometries: JFM article

Flow-structure interactions: PRL article

Micro-transport and Dynamic self-assembly: Springer Book
Flow and heat control applications: JFM article
Parallel computing; Interactive/virtual reality computer graphics: CUP Book

Honors and Awards 

AAAS Fellow, 2018

Alexander von Humboldt Fellow, 2017

ICFDA'16 Riemann-Liouville award, 2016

SIAM's 2015 Ralph E. Kleinman Award

2015 MCS Wiederhielm Award

The USACM J Tinsley Oden Medal, 2013

The USACM Computational Fluid Dynamics Award, 2007

SIAM Fellow 2010

Associate Fellow of the American Institute of Aeronautics & Astronautics (AIAA) 2006

Fellow of the American Physical Society (APS) 2004

Fellow of the American Society of Mechanical Engineers (ASME) 2003

17th Robert Bruce Wallace Lecture Award, MIT, 2003

Rheinstein Junior Faculty Award, Princeton University, 1992


Research featured on the covers of the following publications:

Physical Review Letters (April 2004)
New Scientist (2000)
Science (2000) - featured article
Book on Recent Advances in DNS and LES (Kluwer, 1999)
ACCESS/NCSA (November 1998)
MHPCC'97 (November 1997)
Scientific Computing and Automation (June 1994)
Physics Today (March 1993)
Parity (Japanese, November 1993)

A new report by the National Research Council points to the philosophy and direction of my group, practiced over the last 25 years.  (Thank you NRC!)  Here's a brief sample: "...But the value of the mathematical sciences to the overall science and engineering enterprise and to the nation would be heightened if the number of mathematical scientists who share the following characteristics could be increased: (1) They are knowledgeable across a broad range of the discipline, beyond theirown area(s) of expertise; (2) They communicate well with researchers in other disciplines; (3) They understand the role of the mathematical sciences in the wider world of science, engineering, medicine, defense, and business; and (4) They have some experience with computation..."



Professor Francesco Mainardi


MAY 22 - 31, 2013



JUNE 3 - 5, 2013


Faculty Research Profile

Uncertainty  Quantification AFOSR MURI

Fractional PDEs ARO/MURI