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Record W4205978685 · doi:10.1007/978-0-8176-8394-8_10

Fast Chaotic Artificial Time Integration

2012· book-chapter· en· W4205978685 on OpenAlex
Uri M. Ascher, Kees van den Doel

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

VenueBirkhäuser Boston eBooks · 2012
Typebook-chapter
Languageen
FieldPhysics and Astronomy
TopicModel Reduction and Neural Networks
Canadian institutionsUniversity of British Columbia
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsGradient descentChaoticResidualApplied mathematicsMathematicsNonlinear systemConstant (computer programming)Regularization (linguistics)Method of steepest descentNorm (philosophy)Algebraic numberMathematical optimizationComputer scienceAlgorithmMathematical analysisArtificial neural networkArtificial intelligencePhysics

Abstract

fetched live from OpenAlex

Gradient descent methods for large positive definite linear and nonlinear algebraic systems arise when integrating a PDE to steady state and when regularizing inverse problems. However, these methods may converge very slowly when utilizing a constant step size, or when employing an exact line search at each step, with the iteration count growing proportionally to the condition number. Faster gradient descent methods must occasionally resort to significantly larger step sizes, which in turn yields a strongly nonmonotone decrease pattern in the residual vector norm.In fact, such faster gradient descent methods generate chaotic dynamical systems for the normalized residual vectors. Very little is required to generate chaos here: simply damping steepest descent by a constant factor close to 1 will do. The fastest practical methods of this family in general appear to be the chaotic, two-step ones. Despite their erratic behavior, these methods may also be used as smoothers, or regularization operators. Our results also highlight the need for better theory for these methods.

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), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.882
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0090.003

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 head0.029
GPT teacher head0.232
Teacher spread0.203 · 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