Deep learning and density-functional theory
Bibliographic record
Abstract
We show that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory (DFT) scheme for multielectron systems in simple harmonic oscillator and random external potentials with no feature engineering. We first show that self-consistent charge densities calculated with different exchange-correlation functionals can be used as input to an extensive deep neural network to make predictions for correlation, exchange, external, kinetic, and total energies simultaneously. Additionally, we show that one can make all of the same predictions with the external potential rather than the self-consistent charge density, which allows one to circumvent the Kohn-Sham DFT scheme altogether. We then show that a self-consistent charge density found from a nonlocal exchange-correlation functional can be used to make energy predictions for a semilocal exchange-correlation functional. Lastly, we use a deep convolutional inverse graphics network to predict the charge density given an external potential for different exchange-correlation functionals and assess the viability of the predicted charge densities. This work shows that extensive deep neural networks are generalizable and transferable given the variability of the potentials (maximum total energy range $\ensuremath{\approx}100$ Ha) because they require no feature engineering and because they can scale to an arbitrary system size with an $O(N)$ computational cost.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".