The Environmental Fluid Dynamics Lecture Series
Presents a Seminar
Multi-fidelity Information Fusion Algorithms for
High Dimensional Systems and Massive Data-sets
Dr. George Em Karniadakis
Professor of Applied Mathematics
Brown University
Research Scientist
Massachusetts Institute of
Technology
Tuesday, November 10, 2015
127 Hayes-Healy
11am-12noon
We develop a framework for multi-fidelity information fusion
and predictive inference in high dimensional input spaces and
in the presence of massive data-sets. Hence, we tackle
simultaneously the "big- N" problem for big data and the curseof-dimensionality in multivariate parametric problems. The
proposed methodology establishes a new paradigm for
constructing response surfaces of high dimensional stochastic
dynamical systems, simultaneously accounting for multi-fidelity
in physical models as well as multi-fidelity in probability space.
Scaling to high dimensions is achieved by data-driven
dimensionality reduction techniques based on hierarchical
functional decompositions and a graph-theoretic approach for
encoding custom auto-correlation structure in Gaussian process
priors. Multi-fidelity information fusion is facilitated through
stochastic auto-regressive schemes and frequency-domain
machine learning algorithms that scale linearly with the data.
Taking together these new developments lead to linear
complexity algorithms as demonstrated in benchmark problems
involving deterministic and stochastic fields in up to 100,0000
input dimensions and 100,000 training points on a standard
desktop computer.
Dr. Karniadakis earned his
S.M. and Ph.D. from M.I.T His
research interests include
diverse topics in
computational science both
on algorithms and
applications. A main current
thrust is stochastic
simulations and multiscale
modeling of physical and
biological systems (especially
the brain).