Numerical treatment of stochastic river quality models driven by colored noise
Bibliographic record
Abstract
Monte Carlo simulation is a popular method of risk and uncertainty analysis in oceanographic, atmospheric, and environmental applications. It is common practice to introduce a stochastic part to an already existing deterministic model and, after many simulations, to provide the user with statistics of the model outcome. The underlying deterministic model is often a discretization of a set of partial differential equations describing physical processes such as transport, turbulence, buoyancy effects, and continuity. Much effort is also put into deriving numerically efficient schemes for the time integration. The resulting model is often quite large and complex. In sharp contrast the stochastic extension used for Monte Carlo experiments is usually achieved by adding white noise. Unfortunately, the order of time integration in the stochastic model is reduced compared to the deterministic model because white noise is not a smooth process. Instead of completely replacing the old numerical scheme and implementing a higher‐order scheme for stochastic differential equations, we suggest a different approach that is able to use existing numerical schemes. The method uses a smooth colored noise process as the driving force, resulting in a higher order of convergence. We show promising results from numerical experiments, including parametric uncertainty.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".