Multiscale Stochastic Representations Using Polynomial Chaos Expansions with Gaussian Process Coefficients

  • Charanraj Thimmisetty
  • Fred Aminzadeh
  • Kelly Rose
  • Roger GhanemEmail author
Original Article


We address an important component of risk mitigation for ultra-deep sea drilling in the Gulf of Mexico (GoM), namely the probabilistic characterization of fluid fluxes at the seafloor from future drilling operations. In the process, we develop a stochastic representation of functions defined on a high-dimensional space conditional on their marginal statistics and their global correlation structure. The representation leverages a particular structure of the functional dependence of interest which exhibits scale separation. Specifically, we construct a polynomial chaos representation for scalar quantities of interest whose coefficients are themselves random. The intrinsic randomness of the polynomial chaos expansion (PCE) reflects local uncertainty and captures dependence on a subset of the parameters, while randomness in the PCE coefficients captures a global structure of the uncertainty and dependence on the remaining parameters in the high-dimensional space. This construction is demonstrated by predicting wellbore signatures in the GoM where a 120-dimensional table is populated at several thousand wellbore locations throughout the GoM. Physics-based models of multiphase flow in porous media are used to calculate the PCE representations at the sites where data is available. In this context, random parameters describing the subsurface define the parameter set with respect to which PCE is constructed. A Gaussian process in parameter space is then developed for each coefficient in these representations. The combined probabilistic representation permits the delineation of separate stochastic influences on predictions of interest.



The assistance of Dr. Nima Jabbari and Dr. Arman Khodabakhsh Nejad with the PIPESIM simulations is gratefully acknowledged, as is the assistance of Ms. Corinne Disenhof in formatting the BOEM data to make it spatially referenced. This technical effort was performed in support of the National Energy Technology Laboratory’s ongoing research under Section 999 of the Energy Policy Act of 2005. This publication was prepared in part as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expresses or implies, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference therein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed therein do not necessarily state or reflect those of the United States Government or any agency thereof.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA
  2. 2.University of Southern CaliforniaLos AngelesUSA
  3. 3.National Energy Technology LaboratoryAlbanyUSA

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