Crustal Velocity Field Modelling with Neural Network and Polynomials

  • Khosro Moghtased-Azar
  • Piroska Zaletnyik
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 133)


A comparison of the ability of artificial neural networks and polynomial fitting was carried out in order to model the horizontal deformation field of the Cascadia Subduction Zone, as determined from GPS analyses of the Pacific Northwest Geodetic Array (PANGA).

One set of data was used to calculate the unknown parameters of the model (training set 75 {%} of the whole data set) and the other set was used only for testing the accuracy of the derived model (testing set–25 {%} of the whole data set). The testing set has not been used to determine the parameters of the model.

The problem of overfitting (see Kecman (2001)) (i.e., the substantial oscillation of the model between the training points, the same problem than polynomial wiggle (Mathews and Fink 2004) can be avoided by restricting the flexibility of the neural model. This can be done using an independent data set, namely the validation data (one third part of the training set). The proposed method is the so-called “stopped search method”, which can be used for obtaining a smooth and precise fitting model. However, when fitting high order polynomials, it is difficult to overcome the negative effect of the overfitting problem.

Different order polynomial models and neural network models with different numbers of neurons were calculated. The best fitting polynomial model was 6th order with 28 parameters. The finally used neural network model contained 7 neurons in it’s one hidden layer, with radial basis activation functions, with 31 parameters. These two models, with same order of numbers of parameters, were compared. Calculating the remained errors at the training points the two models had the same fitting precision. However according to the testing point’s results, the neural network model offered more reliable results, with 2–3 times smaller errors.

The computations were performed with the Mathematica software, and the results are given in a symbolic form which can be used in the analysis of crustal deformation, e.g. strain analysis


Crustal deformation Modelling Neural network Polynomial 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Khosro Moghtased-Azar
    • 1
  • Piroska Zaletnyik
    • 2
  1. 1.Department of Geodesy and GeoinformaticsStuttgart UniversityGermany
  2. 2.Department of Geodesy and SurveyingBudapest University of Technology and EconomicsH-1521 Budapest

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