Data-driven model reduction for port-Hamiltonian and network systems in the Loewner framework
Why this work is in the frame
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Bibliographic record
Abstract
The model reduction problem in the Loewner framework for port-Hamiltonian and network systems on graphs is studied. In particular, given a set of right-tangential interpolation data, the (subset of) left-tangential interpolation data that allow constructing an interpolant possessing a port-Hamiltonian structure is characterized. In addition, conditions under which an interpolant retains the underlying port-Hamiltonian structure of the system generating the data are given by requiring a particular structure of the generalized observability matrix. Ipso facto a characterization of the reduced order model in terms of Dirac structure with the aim of relating the Dirac structure of the underlying port-Hamiltonian system with the Dirac structure of the constructed interpolant is given. This result, in turn, is used to solve the model reduction problem in the Loewner framework for network systems described by a weighted graph. The problem is first solved, for a given clustering, by giving conditions on the right- and left-tangential interpolation data that yield an interpolant possessing a network structure. Thereafter, for given tangential data obtained by sampling an underlying network system, we give conditions under which we can select a clustering and construct a reduced model preserving the network structure. Finally, the results are illustrated by means of a second order diffusively coupled system and a first order network system.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it