Koopman-Based Learning of Infinitesimal Generators without Operator Logarithm
Bibliographic record
Abstract
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The challenge remains in providing estimations for transitional properties pertaining to the system's vector fields based on discrete-time observations. To retrieve such infinitesimal system transition information, leveraging the structure of Koopman operator learning, current literature focuses on developing techniques free of time derivatives through the use of the Koopman operator logarithm. However, the soundness of these methods has so far been demonstrated only for maintaining effectiveness within a restrictive function space, together with knowledge of the operator spectrum properties. To better adapt to the practical applications in learning and control of unknown systems, we propose a logarithm-free technique for learning the infinitesimal generator without disrupting the Koopman operator learning framework. This approach claims compatibility with other system verification tools using the same set of training data. We provide numerical examples to demonstrate its effectiveness in applications of system identification and stability prediction.
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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 | 0.000 | 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 | 0.001 |
| 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".