This work presents a machine learning framework for representing exchange–correlation functionals within Density Functional Theory (DFT) [1]. Building on previous approaches in machine learning for exchange–correlation modeling [2,3,4], we introduce a reduced set of physically relevant descriptors to improve interpretability, reduce redundancy, and increase robustness. In addition, the Perdew–Burke–Ernzerhof (PBE) functional [5] is incorporated as a physical constraint to guide the training of deep neural networks and stabilize the optimization process. This physics-informed strategy enables the model to preserve known theoretical behaviors while learning complex data-driven corrections beyond conventional approximations. The combination of dimensionality reduction and embedded physical priors significantly improves training efficiency and mitigates overfitting. Furthermore, it enhances generalization across molecular systems and ensures greater numerical stability during self-consistent field calculations. Results demonstrate improved accuracy in predicting exchange–correlation energies compared to baseline approaches and show conceptual similarities with recent machine learning adaptations of hybrid functionals [6], while relying on a fundamentally different methodology. This work highlights the critical role of combining feature selection and physically grounded constraints for developing reliable and transferable machine learning models in constructing and representing exchange–correlation functionals.

[1] Parr, R. G., Yang, W. Density-Functional Theory of Atoms and Molecules, Oxford University Press (1989).
[2] Cuierrier, E., Roy, P.-O., Ernzerhof, M., J. Chem. Phys. 155, 174121 (2021).
[3] Cuierrier, E., Roy, P.-O., Wang, R., Ernzerhof, M., J. Chem. Phys. 157, 171103 (2022).
[4] Loutis, M., Ernzerhof, M., Roy, P.-O., Manuscript in preparation (2026).
[5] Perdew, J. P., Burke, K., Ernzerhof, M., Phys. Rev. Lett. 77, 3865–3868 (1996).
[6] Khan, D., Price, A. J. A., Huang, B., Ach, M. L., Von Lilienfeld, O. A., Sci. Adv. 11, eadt7769 (2025).