SIMULTANEOUS IDENTIFICATION OF UNKNOWN INITIAL TEMPERATURE AND HEAT SOURCE
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Bibliographic record
Abstract
We investigate in this paper an ill-posed backward heat conduction problem of determining the unknown initial temperature and heat source from given observation at a fixed internal location and the solution value at terminal time. Unlike the classical single parameter identification problems, this ill-posed problem requires the determination of two independent unknown functions from scattered measurement of noisy data. Proof on the uniqueness of the solution is obtained by transforming the original heat conduction equation into an operator equation of the first kind. A new algorithm for the construction of the solution to the backward problem is derived by using the Landweber iteration method for the solution of the corresponding conjugate operator equation. Numerical verification on the efficiency and accuracy of the proposed algorithm is performed by solving several benchmark examples. The proposed method is readily extendable to solve more general multi-parameter identification problems.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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