Machine learning complete intersection Calabi-Yau 3-folds

<jats:p>Gaussian process regression, kernel support vector regression, the random forest, extreme gradient boosting, and the generalized linear model algorithms are applied to data of complete intersection Calabi-Yau threefolds. It is shown that Gaussian process regression is the most suitable for learning the Hodge number <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>h</a:mi><a:mrow><a:mn>2</a:mn><a:mo>,</a:mo><a:mn>1</a:mn></a:mrow></a:msup></a:math> in terms of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>h</c:mi><c:mrow><c:mn>1</c:mn><c:mo>,</c:mo><c:mn>1</c:mn></c:mrow></c:msup></c:math>. The performance of this regression algorithm is such that the Pearson correlation coefficient for the validation set is <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>R</e:mi><e:mn>2</e:mn></e:msup><e:mo>=</e:mo><e:mn>0.9999999995</e:mn></e:math> with a root mean square error <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>R</g:mi><g:mi>M</g:mi><g:mi>S</g:mi><g:mi>E</g:mi><g:mo>=</g:mo><g:mn>0.0002895011</g:mn></g:math>. As for the train set, these two parameters are as follows: <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>R</i:mi><i:mn>2</i:mn></i:msup><i:mo>=</i:mo><i:mn>0.9999999994</i:mn></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>R</k:mi><k:mi>M</k:mi><k:mi>S</k:mi><k:mi>E</k:mi><k:mo>=</k:mo><k:mn>0.0002854348</k:mn></k:math>. The training error and the cross-validation error of this regression are <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>1</m:mn><m:mo>×</m:mo><m:msup><m:mn>10</m:mn><m:mrow><m:mo>−</m:mo><m:mn>9</m:mn></m:mrow></m:msup></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>1.28</o:mn><o:mo>×</o:mo><o:msup><o:mn>10</o:mn><o:mrow><o:mo>−</o:mo><o:mn>7</o:mn></o:mrow></o:msup></o:math>, respectively. Learning the Hodge number <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>h</q:mi><q:mrow><q:mn>1</q:mn><q:mo>,</q:mo><q:mn>1</q:mn></q:mrow></q:msup></q:math> in terms of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>h</s:mi><s:mrow><s:mn>2</s:mn><s:mo>,</s:mo><s:mn>1</s:mn></s:mrow></s:msup></s:math> yields <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mi>R</u:mi><u:mn>2</u:mn></u:msup><u:mo>=</u:mo><u:mn>1.000000</u:mn></u:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>R</w:mi><w:mi>M</w:mi><w:mi>S</w:mi><w:mi>E</w:mi><w:mo>=</w:mo><w:mn>7.395731</w:mn><w:mo>×</w:mo><w:msup><w:mn>10</w:mn><w:mrow><w:mo>−</w:mo><w:mn>5</w:mn></w:mrow></w:msup></w:math> for the validation set of the Gaussian process regression.</jats:p> <jats:sec> <jats:title/> <jats:supplementary-material> <jats:permissions> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material> </jats:sec>

Paper

Similar papers

© 2026 NYSGPT2525 LLC