Surrogate Modeling using Sparse Grids

Abstract: Sparse grid is a technique for constructing multidimensional interpolation rules for purposes of surrogate modeling. Surrogates are used in many applications to replace complex and computationally expensive models with cheap alternatives, which in turn allows addressing questions of sensitivity analysis, model parameter calibration (e.g., using Bayesian inference), optimization, as well as combining several low level models into large multi-physics ones. Sparse grid is an extension of classical one-dimensional interpolation where the multidimensional rule is constructed as a weighted sum of set of tensor rules with different number of points. Interpolation is attractive due to the non-intrusive nature of the approach, which means that the surrogate can be constructed from independent samples of an existing model enabling the use of parallelism and without modifications to the existing code. The tensors used in the sparse grid are carefully chosen to satisfy theoretical estimates for optimality measured in maximum accuracy per number of samples collected from the full model. All methods discussed in the talk are available via the Tasmanian library.

Speaker’s Bio: Miroslav Stoyanov got his Ph.D. from Virginia Tech in 2009. After a post-doc at Florida State University, Dr. Stoyanov joined the Oak Ridge National Laboratory (ORNL) in 2012. His areas of research involve surrogate modeling, uncertainty quantification, high-dimensional approximation, and supercomputing. Dr. Stoyanov is also the lead developer of the ORNL Toolkit for Adaptive Stochastic Modeling and Non-Intrusive Approximation (Tasmanian).