A Posteriori Error Analysis of a Non-Standard Quantity of Interest
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Bibliographic record
Abstract
Classical a posteriori error analysis quantifies error in a Quantity of Interest (QoI) which is represented as a bounded linear functional of the solution. In this work we consider a posteriori error estimates of a specified non-linear quantity of interest using adjoint-based analysis for linear and nonlinear systems of Ordinary Differential Equations. We apply the estimates to the problem of uncertainty quantification of certain example ODEs which depend on a stochastic parameter. In particular, we compute a bound for the error in a corresponding cumulative distribution function. We derive two methods for computing the error estimates for the QoI. The first directly computes the error estimate using linearizations via Taylor's Theorem. The second method acquires our estimate indirectly by implementing root-finding techniques on a corrected solution. We provide several examples to test the accuracy of the methods.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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