Boundary moving horizon estimator for approximate models of parabolic PDEs
Bibliographic record
Abstract
In this work, we focus on the state estimation of the parabolic stochastic partial differential equations (PDEs) with boundary observation. The standard Kalman filter as the optimal estimator with assumption of stochastic process features and known variances on state and output disturbances can not account for the naturally present constraints on the estimated states and state disturbances. Therefore, a motivation to explore the moving horizon estimator (MHE) in the distributed parameter system setting, comes from the idea to synthesize an estimator that provides the best state estimate in a deterministic sense when process and measurement disturbances are with unknown statistics and when process constraints on states and disturbances are present. We explore the parabolic PDEs model with boundary observation, and the spectral decomposition approach is employed to yield a finite dimensional system, which incorporates low dimensional approximation of the original infinite-dimensional system. The boundary moving horizon estimator (MHE) combined with Kalman filter is built to reconstruct accurately the low dimensional approximation of the PDE state based on the noise corrupted boundary observations and estimated bounds arising from the infinite-dimensional parabolic PDEs state representation. The issue of parabolic PDEs state constraints inclusion in the MHE with Kalman filter is demonstrated by relevant simulation study of reaction-diffusion parabolic PDEs process with disturbance constraints and demonstration of accurate PDE state reconstruction.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| 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".