Gamma Distribution Model To Provide a Direct Assessment of the Overall Quality of Quantum Monte Carlo-Generated Electron Distributions
Bibliographic record
Abstract
Our objective is to assess the accuracy of simulated quantum Monte Carlo electron distributions of atoms and molecules. Our approach is first to model the exact electron distribution by a linear combination of gamma distribution functions, with parameters chosen to exactly reproduce highly accurate literature values for a number of selected moments for the system of interest. In application to the ground-state electron distributions of helium and dihydrogen, a high level of accuracy of the model was confirmed upon comparing its predicted moments, not used in the model's parametrization, to those calculated from high-level theory. Next, we generated electron-electron and electron-nucleus distributions for dihydrogen from electron positions outputted from a variety of quantum Monte Carlo algorithms. Upon juxtaposition of the simulated distributions with the putatively exact one that we derived from the model, we quantified the error in simulated distributions. The most accurate distributions were obtained from no-compromise reptation quantum Monte Carlo, a recently developed algorithm designed to ameliorate the distributions' time-step bias. Marginally less accurate distributions were generated from fixed-node diffusion Monte Carlo with descendant counting and detailed balance.
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".