A Kernel-based Machine Learning Approach to Computing Quasiparticle Energies within Many-Body Green's Functions Theory
| Autor: | Tirimbó, Gianluca, Çaylak, Onur, Baumeier, Björn |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We present a Kernel Ridge Regression (KRR) based supervised learning method combined with Genetic Algorithms (GAs) for the calculation of quasiparticle energies within Many-Body Green's Functions Theory. These energies representing electronic excitations of a material are solutions to a set of non-linear equations, containing the electron self-energy (SE) in the $GW$ approximation. Due to the frequency-dependence of this SE, standard approaches are computationally expensive and may yield non-physical solutions, in particular for larger systems. In our proposed model, we use KRR as a self-adaptive surrogate model which reduces the number of explicit calculations of the SE. Transforming the standard fixed-point problem of finding quasiparticle energies into a global optimization problem with a suitably defined fitness function, application of the GA yields uniquely the physically relevant solution. We demonstrate the applicability of our method for a set of molecules from the $GW$100 dataset, which are known to exhibit a particularly problematic structure of the SE. Results of the KRR-GA model agree within less than 0.01 eV with the reference standard implementation, while reducing the number of required SE evaluations roughly by a factor of ten. Comment: 4 pages, 3 figures, conference: Machine Learning for Molecules Workshop at NeurIPS 2020 |
| Databáze: | arXiv |
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