期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 38, 期 4, 页码 B521-B538出版社
SIAM PUBLICATIONS
DOI: 10.1137/15M1055164
关键词
multifidelity modeling; response surfaces; uncertainty quantification; high dimensions; big data; machine learning; Gaussian processes
资金
- DARPA [HR0011-14-1-0060]
- AFOSR [FA9550-12-1-0463]
- Argonne Leadership Computing Facility (ALCF) through the DOE INCITE program
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 10(5) input dimensions and 10(5) training points on a standard desktop computer.
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