Physics-Aware Tuning of Unscented Kalman Filter:Statistical Framework for Solving Inverse Problems Involving Nonlinear Dynamical Systems and Missing Data
Bibliographic record
Abstract
Abstract The performance of the Unscented Kalman Filter (UKF) strongly depends on the proper choice of measurement and process uncertainty matrices, as well as on the scaling parameter of the unscented transform. To avoid cumbersome trial-and-error manual settings in finding the optimal hyperparameters, we introduce a hands-off meta-optimization framework, which incorporates a nonlinear mesh adaptive direct search optimization algorithm in an offline outer loop, paired with a physics-aware loss function. The novelty of this approach is twofold. First, a physics-aware loss function is used to optimize the UKF hyperparameters. It minimizes the physical discrepancy induced by the data-driven correction of the prior states during filtering. Notably, sensor data are not directly incorporated into the calculation of the loss function, which expedites the tuning of the filter in weakly informative data scenarios, especially when the underlying physics is well understood. Second, UKF relaxation is embedded in the optimization to make the measurement and process noise covariance matrices adaptive, which greatly reduces the dimension of the optimization space while remaining very general with respect to the structure of the matrices. We demonstrate the effectiveness of the proposed framework, as the cornerstone of a future digital twin technology combining data- and physics-based models, through various classical problems in solid mechanics, rotating machinery, civil engineering, and fluid-solid interaction.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".