Dresden 2026 – scientific programme

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MM: Fachverband Metall- und Materialphysik

MM 9: Topical Session: Physics-driven Artificial Intelligence for Materials II

MM 9.6: Talk

Monday, March 9, 2026, 17:30–17:45, SCH/A251

Learning exact exchange with symbolic regression — •Noah Hoffmann, Santiago Rigamonti, and Claudia Draxl — Humboldt-Universität zu Berlin, Berlin, Deutschland

Density functional theory (DFT) is the most widely used method for the ab-initio prediction of material properties. It is used for computing structural, vibrational, and electronic properties and more. One important factor influencing the accuracy of the predictions is the choice of the exchange-correlation functional. PBE is the de-facto standard functional because of its good results for ground-state properties at comparatively low computational cost. The most prominent downside of this functional, however, is the underestimation of electronic band gaps. Hybrid functionals like PBE0 compensate this by mixing PBE with the non-local exact-exchange (EXX) energy. This improves band-gaps but comes with a drastic increase in computational cost. We apply symbolic regression (SR), a machine-learning technique, to find inexpensive yet accurate exchange potentials as a surrogate for the EXX potential. This enables computationally efficient DFT calculations with an accuracy close to that of hybrid functionals. To generate the training data for the SR models, we used the optimized effective potential (OEP) method, in which a local approximation to the EXX potential is constructed. The OEP method provides rather accurate electron densities. The SR models are then validated with respect to their numerical stability and their ability to predict band gaps. Compared to PBE, the SR models show improved band gap predictions on OEP band gaps with comparable computational cost.

Keywords: solid state physics; density functional theory; exact exchange; symbolic regression; machine learning