Quantum computing architectures require an accurate and efficient description in terms of many-electron states. Recent implementations include quantum dot arrays, where the ground state of a multi q-bit system can be altered by voltages applied to the top gates. An extensive investigation concerning the spectra of the many-electron systems under multiple operation conditions set by external voltages typically requires a relatively large number of Hamiltonian diagonalizations, where the Coulomb interaction is considered in an exact manner. Instead of making exhaustive calculations using high throughput computing, we approach this problem by augmenting numerical diagonalizations with machine learning techniques designed to predict the many-electron eigenvalues and eigenfunctions. To this end, we employ and compare the results from linear regression methods such as multivariate least squares (MLS) as well as non-linear techniques based on kernel ridge regression (KRR), Gaussian process regression (GPR) and artificial neural networks (ANNs). The input feature vectors are assembled from readily available information comprised from a binary representation of the potential and the strength of the Coulomb interaction. Furthermore, employing a linear classifier, we establish a rule for detecting a singlet-triplet transition which may arise for certain potential configurations.

The paper extends basic Einstein--Hilbert action by adding an invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the space--time geometry and the matter fields. The fundamental Einstein--Hilbert action is extended by considering a generic function ${f}(R,G_{\mu \nu}T^{\mu \nu})$ which is further decomposed into its main constituents, a geometric component which depends on the scalar curvature, and a second element embedding the interplay between geometry and matter fields. Specific cosmological models are established at the level of background dynamics, based on particular couplings between the matter energy--momentum tensor and the Einstein tensor. After deducing the resulting field equations, the physical aspects for the cosmological model are investigated by employing a dynamical system analysis for various coupling functions. The investigation showed that the present model is compatible with different epochs in the evolution of our Universe, possible explaining various late time historical stages.