Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets
Name
Multifidelity information.pdf
Size
7.03 MB
Format
Adobe PDF
Checksum (MD5)
f64860ab856b0f9cc0f51c0ad1e9739d
Author(s)
Venturi, Daniele
Perdikaris, Paris
Karniadakis, George E
Date Issued
July 2016
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Perdikaris, Paris; Venturi, Daniele and Karniadakis, George Em. “Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data Sets.” SIAM Journal on Scientific Computing 38, no. 4 (January 2016): B521–B538 © 2016 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We develop a framework for multifidelity 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 multifidelity in physical models as well as multifidelity 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 autocorrelation structure in Gaussian process priors. Multifidelity information fusion is facilitated through stochastic autoregressive schemes and frequency-domain machine learning algorithms that scale linearly with the data. Taking together these new developments leads to linear complexity algorithms as demonstrated in benchmark problems involving deterministic and stochastic fields in up to 10⁵ input dimensions and 10⁵ training points on a standard desktop computer.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/15M1055164
