Parametric covariance dynamics for the nonlinear diffusive Burgers equation
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Bibliographic record
Abstract
Abstract. The parametric Kalman filter (PKF) is a computationally efficient alternative method to the ensemble Kalman filter. The PKF relies on an approximation of the error covariance matrix by a covariance model with a space–time evolving set of parameters. This study extends the PKF to nonlinear dynamics using the diffusive Burgers equation as an application, focusing on the forecast step of the assimilation cycle. The covariance model considered is based on the diffusion equation, with the diffusion tensor and the error variance as evolving parameters. An analytical derivation of the parameter dynamics highlights a closure issue. Therefore, a closure model is proposed based on the kurtosis of the local correlation functions. Numerical experiments compare the PKF forecast with the statistics obtained from a large ensemble of nonlinear forecasts. These experiments strengthen the closure model and demonstrate the ability of the PKF to reproduce the tangent linear covariance dynamics, at a low numerical cost.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it