Computational Geosciences

, Volume 17, Issue 4, pp 705–721

Reduced order models for many-query subsurface flow applications


    • Lawrence Berkeley National Laboratory 1
  • Yingqi Zhang
    • Lawrence Berkeley National Laboratory 1
  • Stefan Finsterle
    • Lawrence Berkeley National Laboratory 1
Original Paper

DOI: 10.1007/s10596-013-9349-z

Cite this article as:
Pau, G.S.H., Zhang, Y. & Finsterle, S. Comput Geosci (2013) 17: 705. doi:10.1007/s10596-013-9349-z


Inverse modeling involves repeated evaluations of forward models, which can be computationally prohibitive for large numerical models. To reduce the overall computational burden of these simulations, we study the use of reduced order models (ROMs) as numerical surrogates. These ROMs usually involve using solutions to high-fidelity models at different sample points within the parameter space to construct an approximate solution at any point within the parameter space. This paper examines an input–output relational approach based on Gaussian process regression (GPR). We show that these ROMs are more accurate than the linear lookup tables with the same number of high-fidelity simulations. We describe an adaptive sampling procedure that automatically selects optimal sample points and demonstrate the use of GPR to a smooth response surface and a response surface with abrupt changes. We also describe how GPR can be used to construct ROMs for models with heterogeneous material properties. Finally, we demonstrate how the use of a GPR-based ROM in two many-query applications—uncertainty quantification and global sensitivity analysis—significantly reduces the total computational effort.


Surrogate modelsGaussian process regressionHydrogeologyUncertainty quantification

Copyright information

© Springer Science+Business Media Dordrecht (outside the USA) 2013