A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Kontolati, Katiana; Loukrezis, Dimitrios; Giovanis, Dimitrios G.; Vandanapu, Lohit; Shields, Michael D.

doi:10.1016/j.jcp.2022.111313

Title: A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Journal Article · Mon May 23 00:00:00 EDT 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.111313· OSTI ID:1906444

Kontolati, Katiana ^[1]; Loukrezis, Dimitrios ^[2]; Giovanis, Dimitrios G. ^[1]; Vandanapu, Lohit ^[1]; Shields, Michael D. ^[1]

Johns Hopkins Univ., Baltimore, MD (United States)
Darmstadt Univ. of Technology (Germany); Siemens AG, Munich (Germany)

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10ⁿ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

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Research Organization:: Johns Hopkins Univ., Baltimore, MD (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0020428

OSTI ID:: 1906444

Alternate ID(s):: OSTI ID: 1870935

Journal Information:: Journal of Computational Physics, Vol. 464; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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