  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.
