Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support
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 e...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1600 |
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| author | Francisco José Navarro-González Yolanda Villacampa Mónica Cortés-Molina Salvador Ivorra |
| author_facet | Francisco José Navarro-González Yolanda Villacampa Mónica Cortés-Molina Salvador Ivorra |
| author_sort | Francisco José Navarro-González |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T16:16:25Z |
| format | Article |
| id | doaj.art-88268b744d6e4008846d6f7f53356acb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:16:25Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-88268b744d6e4008846d6f7f53356acb2023-11-20T14:02:44ZengMDPI AGMathematics2227-73902020-09-0189160010.3390/math8091600Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh SupportFrancisco José Navarro-González0Yolanda Villacampa1Mónica Cortés-Molina2Salvador Ivorra3Department of Applied Mathematics, University of Alicante, 03690 Alicante, SpainDepartment of Applied Mathematics, University of Alicante, 03690 Alicante, SpainDepartment of Applied Mathematics, University of Alicante, 03690 Alicante, SpainDepartment of Civil Engineering, University of Alicante, 03690 Alicante, SpainEstimation 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.https://www.mdpi.com/2227-7390/8/9/1600numerical modellingalgorithmradial kernelslocal mesh supportnon-linear models |
| spellingShingle | Francisco José Navarro-González Yolanda Villacampa Mónica Cortés-Molina Salvador Ivorra Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support Mathematics numerical modelling algorithm radial kernels local mesh support non-linear models |
| title | Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support |
| title_full | Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support |
| title_fullStr | Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support |
| title_full_unstemmed | Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support |
| title_short | Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support |
| title_sort | numerical non linear modelling algorithm using radial kernels on local mesh support |
| topic | numerical modelling algorithm radial kernels local mesh support non-linear models |
| url | https://www.mdpi.com/2227-7390/8/9/1600 |
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