Reinforced Data-Driven Estimation for Spectral Properties of Koopman Semigroup in Stochastic Dynamical Systems
Bibliographic record
Abstract
Koopman spectral analysis turns nonlinear stochastic dynamics into a linear evolution of observables and gives access to decay rates, oscillatory modes, and metastable behavior. In practice, however, EDMD, SDMD, and related estimators depend strongly on where the trajectory data are collected. If most trajectories start in regions that carry little spectral information, the leading eigenvalues and eigenfunctions can be poorly estimated even with a rich dictionary. We propose \emph{Reinforced SDMD}, a data-acquisition method that couples Stochastic Dynamic Mode Decomposition with reinforcement learning. The RL agent chooses trajectory-initialization regions, SDMD updates the Koopman approximation, and a spectral-consistency reward evaluates the estimated eigenpairs on the newly generated data. An exploration bonus is added to avoid repeatedly sampling only a small part of the state space. We test multi-armed bandits, DQN, and PPO on stochastic double-well, Duffing, and FitzHugh--Nagumo systems. The learned policies place more samples in regions that are useful for estimating the leading Koopman eigenpairs. We also give an error-propagation analysis showing how SDMD operator error enters the corresponding bandit, approximate value-iteration, and approximate policy-iteration bounds.
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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 | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".