A PRIORI ERROR ANALYSIS OF STOCHASTIC GALERKIN PROJECTION SCHEMES FOR RANDOMLY PARAMETRIZED ORDINARY DIFFERENTIAL EQUATIONS
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Bibliographic record
Abstract
Generalized polynomial chaos (gPC) based stochastic Galerkin methods are widely used to solve randomly parametrized ordinary differential equations (RODEs). These RODEs are parametrized in terms of a finite number of independent and identically distributed second-order random variables. In this paper, we derive a priori error estimates for stochastic Galerkin approximations of RODEs accounting for the temporal and stochastic discretization errors. Under appropriate stochastic regularity assumptions, convergence rates are provided for first-order linear RODE systems and first-order nonlinear scalar RODEs. We also consider the case of second-order linear RODE systems that are routinely encountered in stochastic structural dynamics applications. Finally, some insights into the long-time behavior of gPC schemes are provided for a model problem drawing on the present analysis.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.021 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it