Multi-fidelity Information Fusion Algorithms for High Dimensional Systems and Massive Data-sets

10-23-2014

The second lecture in the Center for Computational and Applied Mathematics Distinguished Lecture Series will be held at 3:30 pm on Monday, Nov. 2, 2015 in LWSN 1142.  Prof. George Em Karniadakis of Brown University will present the lecture titled "Multi-fidelity Information Fusion Algorithms for High Dimensional Systems and Massive Data-sets." Refreshments will be served outside the lecture hall at 3 pm.

Abstract: 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 curse-of-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.

George KarniadakisGeorge Em Karniadakis is the Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics at Brown University, and the director of the DOE Center of Mathematics for Mesoscale Modeling of Materials (CM4). He is Fellow of SIAM (2010), APS (2004) and ASME (2003) and Associate Fellow of AIAA (2006).

His current research interests are in stochastic multiscale modeling, and is widely known for his fundamental contributions on high-dimensional stochastic modeling and multiscale simulations of physical and biological systems.

His most recent awards include SIAM’s Ralph E Kleinman Award (2015) for “many outstanding contributions to Applied Mathematics in a broad range of areas, including computational fluid dynamics, spectral methods and stochastic modeling”, and the MCS Wiederhielm Award (2015) “for the most highly cited original article in Micro-circulation over the previous five year period for the paper, Blood Flow and Cell-Free Layer in Microvessels.”