Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank
(2021)
*Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry.*
Machine Learning: Science and Technologie, 2
.
pp. 1-23.

Full text not available from this repository.

Official URL: https://doi.org/10.1088/2632-2153/ac14ad

## Abstract

We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the reproducing kernel Hilbert spaces induced by symmetric and antisymmetric Gaussian kernels are dense in the space of symmetric and antisymmetric functions, and propose a Slater determinant representation of the antisymmetric Gaussian kernel, which allows for an efficient evaluation even if the state space is high-dimensional. Furthermore, we show that by exploiting symmetries or antisymmetries the size of the training data set can be significantly reduced. The results are illustrated with guiding examples and simple quantum physics and chemistry applications.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2808 |

Deposited By: | Monika Drueck |

Deposited On: | 18 Mar 2022 10:42 |

Last Modified: | 18 Mar 2022 10:42 |

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