Machine learning out-of-equilibrium correlations in the Bose-Hubbard model
Bibliographic record
Abstract
Calculating the out-of-equilibrium dynamics of many-body quantum systems theoretically is a challenging problem. Essentially exact results can be obtained for the out-of-equilibrium correlations in the Bose-Hubbard model in one dimension, but higher dimensions require approximate methods. One such method is the two-particle irreducible strong coupling (2PISC) approach [M. R. C. Fitzpatrick and M. P. Kennett, Nucl. Phys. B 930, 1 (2018)]. Calculations of the single-particle correlations using this method yield values of the velocity for correlation spreading that match well with exact methods in one dimension and experiments in one and two dimensions. However, the 2PISC method is less accurate for determining the amplitude of correlations, especially in the regime where interactions are not very strong. Viewing the calculation of the single-particle correlations as an image correction problem, we train a neural network (NN) to take input from the 2PISC approach to reproduce the output of exact diagonalization calculations. We show that the predictions of the NN improve on 2PISC results for parameters outside the training region. Our approach is not specific to the Bose-Hubbard model and may find application to the out-of-equilibrium dynamics of other quantum many-body systems.
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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) | 0.000 | 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 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".