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Model Dimension Reduction

In: Model Calibration and Parameter Estimation

Author

Listed:
  • Ne-Zheng Sun

    (University of California at Los Angeles, Department of Civil and Environmental Engineering)

  • Alexander Sun

    (University of Texas at Austin, Bureau of Economic Geology, Jackson School of Geosciences)

Abstract

A real system, especially a distributed parameter system, may havehigh or even infinite dimensions of freedom (DOF). When the DOF ofa model is too high, all inversion methods that we have learnedbecome inefficient and the inverse problem becomes unsolvablebecause of data and computational limitations. On the other hand,when the structure of a model is overly simplified, the model maybecome useless because of its large structure error. An appropriatemodel complexity depends not only on the complexity of the modeledsystem, but also on data availability, data format, and the intendeduse of the model. The main purpose of this chapter is to give acomprehensive survey of various parameterization techniques, suchas Voronoi diagram, radial basis functions, and local polynomialapproximation for representing deterministic functions, and Gaussianrandom field, Markov random field, variogram analysis, andmultipoint statistics for representing stochastic fields. Linear andnonlinear model dimension reduction methods, such as POD, FA,and kernel PCA, are considered and applied to model inversion.

Suggested Citation

  • Ne-Zheng Sun & Alexander Sun, 2015. "Model Dimension Reduction," Springer Books, in: Model Calibration and Parameter Estimation, edition 127, chapter 6, pages 185-245, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-2323-6_6
    DOI: 10.1007/978-1-4939-2323-6_6
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