Identifiability of Linear Time-Invariant Differential-Algebraic Systems. I. The Generalized Markov Parameter Approach
Bibliographic record
Abstract
A mathematical model is identifiable if and only if there is a unique relationship between each parameter value and the input−output behavior of the model. If a model is not identifiable, there is no unique solution to the parameter estimation problem, regardless of the number and types of experiments that are performed. A new method for testing the identifiability of linear time-invariant (LTI) differential-algebraic systems is presented. This method is an extension of the Markov parameter method, proposed by Grewal and Glover ( IEEE Trans. Autom. Control 1976, 21, 833) and Vajda ( Sci. Pap. Inst. Tech. Cybernetics Tech. Univ. Wroclaw 1985, 29, 228) for LTI ordinary differential equation systems. In the proposed method, the differential-algebraic system is partitioned into an ordinary differential equation subsystem and an algebraic subsystem. This allows for the computation of structural invariants called the generalized Markov parameters (GMPs). A system is identifiable if and only if the dependence of the GMPs on the parameters is one-to-one almost everywhere on the allowable parameter set. Tests for global and local identifiability are developed. The application of this method is demonstrated using two examples including an idealized gas-phase reactor.
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How this classification was reachedexpand
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 | 0.002 | 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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".