<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1794-6190</journal-id>
<journal-title><![CDATA[Earth Sciences Research Journal]]></journal-title>
<abbrev-journal-title><![CDATA[Earth Sci. Res. J.]]></abbrev-journal-title>
<issn>1794-6190</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1794-61902021000400371</article-id>
<article-id pub-id-type="doi">10.15446/esrj.v25n4.91195</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study]]></article-title>
<article-title xml:lang="es"><![CDATA[Predicción de ondulación geoide con Redes Neuronales Artificiales (base radial y regresión generalizada), regresión lineal múltiple y métodos de interpolación: estudio comparativo]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Konakoglu]]></surname>
<given-names><![CDATA[Berkant]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Akar]]></surname>
<given-names><![CDATA[Alper]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Amasya University Technical Sciences Vocational School ]]></institution>
<addr-line><![CDATA[Amasya ]]></addr-line>
<country>Turkey</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Erzincan Binali Yildinm University Vocational School ]]></institution>
<addr-line><![CDATA[Erzincan ]]></addr-line>
<country>Turkey</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>25</volume>
<numero>4</numero>
<fpage>371</fpage>
<lpage>382</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1794-61902021000400371&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1794-61902021000400371&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1794-61902021000400371&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT This study evaluated different methods for geoid undulation prediction and included two types of artificial neural networks (ANNs) - the radial basis function neural network (RBFNN) and the generalized regression neural network (GRNN) - as well as conventional methods including multiple linear regression (MLR) and ten different interpolation techniques. In this work, k-fold cross-validation was used to evaluate the model and its behavior on the independent dataset. With this validation method, each of a k number of groups has the chance to be divided into training and testing data. The performances of the methods were evaluated in terms of the root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe efficiency coefficient (NSE), correlation coefficient (R2), and using graphical indicators. The evaluation of the performance of the datasets obtained using cross-validation was performed in two ways. When the method having the minimum error result was accepted as the most appropriate method, the natural neighbor (NN) gave better results than the other methods (RMSE = 0.142 m, MAE = 0.097 m, NSE = 0.98986, and R2 = 0.99011). On the other hand, it was observed that on average, the GRNN exhibited the best performance (RMSE = 0.185 m, MAE = 0.137 m, NSE = 0.98229, and R2 = 0.98249).]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Este estudio evalúa los métodos diferentes de predicción de ondulación geoide donde se incluye dos tipos de Redes Neuronales Artificiales -la red neuronal de base radial y la red neuronal de regresión generalizada- al igual que métodos convencionales donde se incluyen la regresión lineal múltiple y diez técnicas diferentes de interpolación. En este trabajo, la validación cruzada de K iteraciones se usó para evaluar el modelo y su comportamiento en un conjunto de datos independiente. Con este método de evaluación, cada grupo de números k tiene la posibilidad de dividirse entre datos de entrenamiento y datos de evaluación. El desempeño de los métodos se evaluó en términos de la raíz del error cuadrático medio (RMSE, del inglés root mean square error), el error absoluto medio (MAE, mean absolute error), el coeficiente de eficiencia Nash-Sutcliffe (NSE, Nash-Sutcliffe efficiency coefficient) y el coeficiente de correlación (R2, correlation coefficient) a través de indicadores gráficos. La evaluación del desempeño de los grupos de datos obtenidos con la validación cruzada se realizó en dos vías. Cuando el método que tiene el resultado de mínimo error es aceptado como el método más apropiado, el vecino natural ofrece mejores resultados que otros métodos (RMSE = 0.142 m, MAE = 0.097 m, NSE = 0.98986, and R2 = 0.99011). Por otro lado, se observó que en promedio la red neuronal de regresión generalizada presentó un mejor desempeño (RMSE = 0.185 m, MAE = 0.137 m, NSE = 0.98229, and R2 = 0.98249).]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Generalized regression neural network (GRNN)]]></kwd>
<kwd lng="en"><![CDATA[Radial basis function neural network (RBFNN)]]></kwd>
<kwd lng="en"><![CDATA[Multiple linear regression (MLR)]]></kwd>
<kwd lng="en"><![CDATA[Interpolation methods]]></kwd>
<kwd lng="en"><![CDATA[Geoid determination]]></kwd>
<kwd lng="es"><![CDATA[red neuronal de regresión generalizada]]></kwd>
<kwd lng="es"><![CDATA[red neuronal de base radial]]></kwd>
<kwd lng="es"><![CDATA[regresión lineal múltiple]]></kwd>
<kwd lng="es"><![CDATA[métodos de interpolación]]></kwd>
<kwd lng="es"><![CDATA[determinación geoide]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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