Electronic Structure Reading Group: Uncertainty-aware functional distributions

Density functional theory (DFT) is widely used for understanding material properties and chemical reactions. DFT simulations use approximations which result in errors when comparing to experiments. There are errors in different types of energies, lattice constants and other properties. Quantitative uncertainty estimates would be helpful for DFT simulations to highlight which results are trustworthy. Quantifying uncertainties not only improves trust in calculations but also identifies high-uncertainty predictions that can subsequently be revisited and reanalyzed.

We propose a method to model uncertainties using a probability distribution over exchange-correlation functionals. The probability distribution is trained on experimental values of molecular atomization energies, cohesive energies of solids, lattice constants, and bulk moduli. The optimized probability distribution is then used to estimate the bias and variance on simulated materials properties.

The proposed method is general enough to be applied to any simulation methodology where accurate reference benchmarks exist.

Citations: 
Pre-print: https://arxiv.org/abs/2504.11070
BEEF: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.235149
BEEF chapter for reading: https://www.sciencedirect.com/science/article/pii/B9780081029411000031

This event is jointly organized with the COSMO seminar.
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The electronic structure reading group brings together researchers and students interested in mathematical aspects of electronic structure problems and adjacent topics, including:

• Density Functional Theory
• Many-body Schrödinger equation for electrons
• Born-Oppenheimer Molecular Dynamics
• Numerical analysis and error control