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Bayesian Koopman Time Series Forecasting

2025· article· W7135090694 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

Venuenot available
Typearticle
Language
FieldComputer Science
TopicGaussian Processes and Bayesian Inference
Canadian institutionsMcGill University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsPrior probabilityOperator (biology)Bayesian probabilityBayesian inferenceNonlinear systemSampling (signal processing)Set (abstract data type)Series (stratigraphy)Dynamical systems theoryLinear map

Abstract

fetched live from OpenAlex

We propose a framework for time series prediction that leverages Koopman operator theory, a powerful tool for capturing nonlinear dynamical systems through linear evolution via transformation to a high dimensional space. By approximating the Koopman operator using a finite set of basis functions, we transform the forecasting problem into linearized propagation of observables. To account for parameter uncertainty, we adopt a Bayesian approach to infer the parameters of the approximate Koopman operator, enabling posterior sampling over dynamics. Our model incorporates prior knowledge via explicit parameter priors and performs inference by sampling from the posterior. The resulting Bayesian Koopman operator can be implemented with standard deep learning architectures such as linear recurrent neural networks. We demonstrate its advantages on complex dynamical systems, comparing performance to standard deterministic Koopman baselines.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Scholarly communication, Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.836
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.002
Science and technology studies0.0010.000
Scholarly communication0.0020.002
Open science0.0020.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0020.001

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.

Opus teacher head0.013
GPT teacher head0.230
Teacher spread0.218 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it