Bayesian Error Estimation in Density-Functional Theory
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We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.
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Empirically, models with more than roughly eight parameters are often recognizably sloppy.
“Empirically we find, from studying a variety of models [3, 4, 7] as well as subsystems of models (like PC12 in Figure 1 (a)) [18], that models with more than roughly eight parameters are often recognizably sloppy.”
From Sloppy-model universality class and the Vandermonde matrix. (2006) · cites this paper as [4]
Systems with many parameters are often sloppy: their behavior depends only on a few stiff combinations of parameters and is unchanged as other sloppy parameter combinations vary by orders of magnitude.
“Systems with many parameters are often sloppy . For practical purposes their behavior depends only on a few stiffly constrained combinations of the parameters; other directions in parameter space can change by orders of magnitude without significantly changing the behavior.”
From Sloppy-model universality class and the Vandermonde matrix. (2006) · cites this paper as [4]
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- Authors
- Mortensen, J. J., Kaasbjerg, K., Frederiksen, S. L., Nørskov, J. K., Sethna, J. P., & Jacobsen, K. W.
- Affiliations
- Technical University of Denmark (DK)
- Cornell University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-11-15
- Volume
- 95
- Issue
- 21
- Pages
- 216401-216401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2024745355
- Cited by
- 208
- References
- 36
- Citations by year
- 2026: 11 · 2025: 5 · 2024: 17 · 2023: 6 · 2022: 14 · 2021: 14 · 2020: 23 · 2019: 15 · 2018: 17 · 2017: 13 · 2016: 19 · 2015: 7 · 2014: 5 · 2013: 5 · 2012: 8
- FWCI
- 1.84
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- error estimation, density functional theory, exchange-correlation functionals, Bayesian ensemble, binding energy, bond lengths, vibrational frequencies, functional benchmarking, comparison with experimental data
- MeSH terms
- Bayes Theorem, Models, Biological, Models, Chemical
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