Reduced order parameter estimation using quasilinearization and quadratic programming

Authors

  • Adam J. Siade,

    1. Department of Civil and Environmental Engineering, University of California,Los Angeles, California,USA
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  • Mario Putti,

    1. Department of Mathematical Methods and Models for Scientific Applications, University of Padua,Padua,Italy
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  • William W.-G. Yeh

    Corresponding author
    1. Department of Civil and Environmental Engineering, University of California,Los Angeles, California,USA
      Corresponding author: W. W.-G Yeh, Department of Civil and Environmental Engineering, University of California, 405 Hilgard Ave., Los Angeles, CA 90095, USA. (williamy@seas.ucla.edu)
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Corresponding author: W. W.-G Yeh, Department of Civil and Environmental Engineering, University of California, 405 Hilgard Ave., Los Angeles, CA 90095, USA. (williamy@seas.ucla.edu)

Abstract

[1] The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.

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