pykoop: a Python Library for Koopman Operator Approximation
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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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.099 | 0.042 |
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".