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Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support

Author

Listed:
  • Francisco José Navarro-González

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Yolanda Villacampa

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Mónica Cortés-Molina

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Salvador Ivorra

    (Department of Civil Engineering, University of Alicante, 03690 Alicante, Spain)

Abstract

Estimation problems are frequent in several fields such as engineering, economics, and physics, etc. Linear and non-linear regression are powerful techniques based on optimizing an error defined over a dataset. Although they have a strong theoretical background, the need of supposing an analytical expression sometimes makes them impractical. Consequently, a group of other approaches and methodologies are available, from neural networks to random forest, etc. This work presents a new methodology to increase the number of available numerical techniques and corresponds to a natural evolution of the previous algorithms for regression based on finite elements developed by the authors improving the computational behavior and allowing the study of problems with a greater number of points. It possesses an interesting characteristic: Its direct and clear geometrical meaning. The modelling problem is presented from the point of view of the statistical analysis of the data noise considered as a random field. The goodness of fit of the generated models has been tested and compared with some other methodologies validating the results with some experimental campaigns obtained from bibliography in the engineering field, showing good approximation. In addition, a small variation on the data estimation algorithm allows studying overfitting in a model, that it is a problematic fact when numerical methods are used to model experimental values.

Suggested Citation

  • Francisco José Navarro-González & Yolanda Villacampa & Mónica Cortés-Molina & Salvador Ivorra, 2020. "Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support," Mathematics, MDPI, vol. 8(9), pages 1-27, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1600-:d:414835
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    References listed on IDEAS

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    1. Mohamed Machkouri, 2007. "Nonparametric Regression Estimation for Random Fields in a Fixed-Design," Statistical Inference for Stochastic Processes, Springer, vol. 10(1), pages 29-47, January.
    2. Oliveira, Victor De, 2000. "Bayesian prediction of clipped Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 299-314, September.
    3. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
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