George Em Karniadakis
"People who wish to analyze nature without using mathematics must settle for a reduced understanding." Richard Feynman
The Charles Pitts Robinson and John Palmer Barstow
Professor of Applied Mathematics
Research Scientist, Massachusetts Institute of Technology
Room 312, 170 Hope Street
Phone: +1 401 863 1217
George_Karniadakis@Brown.edu
Ph.D., Massachusetts Institute of Technology, 1987
Teaching
Biography
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 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 Ralf E Kleinman award from SIAM (2015), the (inaugural) J. Tinsley Oden Medal (2013), and the CFD award (2007) by the US Association in Computational Mechanics. His hindex is 85 and he has been cited over 36,500 times (see his google scholar citations). See complete CV here. You can also check out his Geneaology Tree (remember to zoom in!). Here is his wikepedia profile.
 Karniadakis is currently the lead PI of an OSD/ARO/MURI on Fractional PDEs, and previously the lead PI of an OSD/AFOSR MURI on Uncertainty Quantification. He is also the Director of the DOE Center of Mathematics for Mesoscale Modeling of Materials (CM4).
Research Interests
His current research interests are on machine learning for scientific computing, 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, CiSE, JCP
Biophysics  Multiscale modeling of biological systems: PNAS (sickle cell anemia); PNAS (blood viscosity); PNAS (malaria) article; PNAS (thrombosis) article, PRS article
Atomistic/Mesoscopic modeling  Dissipative Particle Dynamics: JCP (tripledecker); 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
Flowstructure interactions: PRL article
Microtransport and Dynamic selfassembly: Springer Book Flow and heat control applications: JFM article Parallel computing; Interactive/virtual reality computer graphics: CUP Book
Honors and Awards
ICFDA'16 RiemannLiouville 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
Publications
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..." 
Links
SHORT COURSE: AN INTRODUCTION TO FRACTIONAL CALCULUS Professor Francesco Mainardi 

SHORT COURSE ON FRACTIONAL PDES MAY 22  31, 2013 

INTERNATIONAL SYMPOSIUM ON FRACTIONAL PDES: THEORY, NUMERICS AND APPLICATIONS JUNE 3  5, 2013 