Dynamic regression in tracking of chaotic system trajectories
Bibliographic record
Abstract
A kernel-based batch approach to trajectory estimation of nonlinear dynamical systems based on measured system output is presented.The model is assumed unknown, while a local surrogate model is hypothesized instead that evolves in time while adapting itself to best fit the observed output data stream.The local model is assumed to be a multivariate LTI system whose adaptation is achieved in terms of repetitive solution of a local ridge regression problem.The latter is rendered dynamic by introducing an additional penalty which effectively allows to identify the underlying autoregressive trend in the parameters of the surrogate model.The idea bears a slight resemblance to dynamic ridge regression used in econometric identification of nonlinear time series, state space regression with drift, and minimum energy estimation.A kernel representation of multivariate LTI systems is proposed, which enables high accuracy batch processing of measured system output data towards achieving nonasymptotic, joint estimation of system parameters and states in a local system model.The efficiency of the approach is demonstrated in application to tracking of the state of a planar four-state and two-output chaotic system: a frictionless double pendulum whose model is unknown.The method presented is expected to prove helpful in the design of novel approaches to non-parametric, non-asymptotic nonlinear state and parameter estimation. RésuméUne méthode pour l'estimation de la trajectoire de systèmes dynamiques non linéaires basée sur la sortie du système mesurée est présentée.L'approche emploie la théorie de les noyaux reproduisants.Le modèle est supposé inconnu, tandis qu'un modèle de substitution local est mise en place qui évolue dans le temps tout en s'adaptant au mieux au flux de données de sortie observé.Le modèle local est supposé être un système LTI multivarié dont l'adaptation est obtenue en termes de solution répétitive d'un problème de régression.Ce dernier est rendu dynamique en introduisant une pénalité supplémentaire qui permet effectivement d'identifier la tendance autorégressive sous-jacente dans les paramètres du modèle de substitution.L'idée présente une légère ressemblance avec la régression dynamique de la crête utilisée dans l'identification économétrique des séries temporelles nonlinéaires.Une représentation du noyau des systèmes LTI multivariés est proposée, qui permet le traitement par lots de haute précision des données de sortie du système mesurées.Une estimation conjointe non asymptotique des paramètres et des états du système est effectuée.L'efficacité de l'approche est démontrée dans l'application au suivi de l'état d'un système chaotique planaire à quatre états et deux sorties: un double pendule sans frottement dont le modèle est inconnu.La méthode présentée devrait s'avérer utile dans la conception de nouvelles approches de l'estimation non-paramétrique et non-asymptotique.Contents 0.1 Background and Most Relevant Literature . . . . . .
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".