Discrete Kalman Filter Design for Kuramoto-Sivashinsky Equation
Bibliographic record
Abstract
Kuramoto-Sivashinsky partial differential equation (KSE) has attracted a lot of attention from academia and industry due to its ability to describe various physical phenomena associated with both wave and propagation wave front dynamics. This work addresses infinite-dimensional discrete-time Kalman filter design for KSE by applying a state-of-the-art Crank-Nicolson discretization framework which does not account for spatial approximation or order reduction of the underlying model. A novel infinite-dimensional discrete-time Crank-Nicolson discretization is provided and utilized for KSE discretization in time, which is amenable to the ensuing discrete Kalman filter design. In addition, a two-step infinite-dimensional discrete-time Kalman filter is developed for the state estimation of KSE model augmented with the state and measurement noises. Finally, the effectiveness of the presented discrete-time Kalman filter is investigated and validated by simulations.
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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 | 0.001 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".