In this work, Gaussian process regression (GPR) models are employed to emulate ab initio atomic data for multielectron systems, generated using the multiconfiguration Dirac-Hartree-Fock method. The $4f^2$ systems serve as a test case, where strongly correlated $f$ orbitals can lead to significant changes in atomic properties along the isoelectronic sequence. Energy levels and transition probabilities are calculated by including relativistic effects, electron correlations, Breit, and quantum electrodynamic corrections, and are then used to train the GPR model. The trained model is subsequently used to predict properties of unknown elements along the isoelectronic sequence, including important estimates of uncertainties. The agreement between the theoretical values and the GPR results is within the predicted uncertainties for most of the data, confirming the reliability of the model outputs. The GPR model also demonstrates its ability to predict energy levels unseen in the training data by capturing correlations between $Z$ and atomic states $\left({}^{2S+1}L_J\right)$ within the $4f^2$ manifold.

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• Atomic & molecular structure
• Atomic spectra
• Electron correlation calculations for atoms & ions
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions