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Record W2992614702 · doi:10.1093/mnras/staa240

Embedded operator splitting methods for perturbed systems

2020· article· en· W2992614702 on OpenAlex
Hanno Rein

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

VenueMonthly Notices of the Royal Astronomical Society · 2020
Typearticle
Languageen
FieldMathematics
TopicNumerical methods for differential equations
Canadian institutionsThe Scarborough HospitalUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsPhysicsOperator (biology)AstronomyAstrophysicsGenetics

Abstract

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ABSTRACT It is common in classical mechanics to encounter systems whose Hamiltonian H is the sum of an often exactly integrable Hamiltonian H0 and a small perturbation ϵH1 with ϵ ≪ 1. Such near-integrability can be exploited to construct particularly accurate operator splitting methods to solve the equations of motion of H. However, in many cases, for example in problems related to planetary motion, it is computationally expensive to obtain the exact solution to H0. In this paper, we present a new family of embedded operator splitting (EOS) methods which do not use the exact solution to H0, but rather approximate it with yet another, EOS method. Our new methods have all the desirable properties of classical methods which solve H0 directly. But in addition they are very easy to implement and in some cases faster. When applied to the problem of planetary motion, our EOS methods have error scalings identical to that of the often used Wisdom–Holman method but do not require a Kepler solver, nor any coordinate transformations, or the allocation of memory. The only two problem specific functions that need to be implemented are the straightforward kick and drift steps typically used in the standard second-order leap-frog method.

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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)0.001
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: Simulation or modeling
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.189
Threshold uncertainty score0.640

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.064
GPT teacher head0.351
Teacher spread0.287 · 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