High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

Journal Article · 10 October 2017 · Mathematical Geosciences

DOI: https://doi.org/10.1007/s11004-017-9705-y · OSTI ID:1400095

Thimmisetty, Charanraj A. ^[1]; Ghanem, Roger G. ^[2]; White, Joshua A. ^[3]; Chen, Xiao ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
2. Univ. of Southern California, Los Angeles, CA (United States). Sonny Astani Dept. of Civil and Environmental Engineering
3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division

This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. It relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1400095
• Report Number(s): LLNL-JRNL-728760; TRN: US1703098
• Journal Information: Mathematical Geosciences, Vol. 50, Issue 1; ISSN 1874-8961
• Publisher: SpringerCopyright Statement
• Country of Publication: United States
• Language: English