pykoop: a Python Library for Koopman Operator Approximation
Why this work is in the frame
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Bibliographic record
Abstract
pykoop is a Python package for learning differential equations in discretized form using the Koopman operator.Differential equations are an essential tool for modelling the physical world.Ordinary differential equations can be used to describe electric circuits, rigid-body dynamics, or chemical reaction rates, while the fundamental laws of electromagnetism, fluid dynamics, and heat transfer can be formulated as partial differential equations.The Koopman operator allows nonlinear differential equations to be rewritten as infinite-dimensional linear differential equations by viewing their time evolution in terms of an infinite number of nonlinear lifting functions.A finite-dimensional approximation of the Koopman operator can be identified from data given a user-selected set of lifting functions.Thanks to its linearity, the approximate Koopman model can be used for analysis, design, and optimal controller or observer synthesis for a wide range of systems using well-established linear tools.pykoop's documentation, along with examples in script and notebook form, can be found at at pykoop.readthedocs.io/en/stable.Its releases are also archived on Zenodo (Dahdah & Forbes, 2024b).
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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 | 0.001 |
| Open science | 0.001 | 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