Leveraging normalizing flows for orbital-free density functional theory
Bibliographic record
Abstract
Abstract Orbital-free density functional theory (OF-DFT) for real-space systems has historically depended on Lagrange optimization techniques, primarily due to the inability of previously proposed electron density approaches to ensure the normalization constraint. This study illustrates how leveraging contemporary generative models, notably normalizing flows (NFs), can surmount this challenge. We develop a Lagrangian-free optimization framework by employing these machine learning models for the electron density. This diverse approach also integrates cutting-edge variational inference techniques and equivariant deep learning models, offering an innovative reformulation to the OF-DFT problem. We demonstrate the versatility of our framework by simulating a one-dimensional diatomic system, LiH, and comprehensive simulations of hydrogen, lithium hydride, water, and four hydrocarbon molecules. The inherent flexibility of NFs facilitates initialization with promolecular densities, markedly enhancing the efficiency of the optimization process.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".