Three optimization formulations for an inverse problem in saddle point problems with applications to elasticity imaging of locating tumor in incompressible medium
Bibliographic record
Abstract
This work focuses on identifying a distributed parameter in a saddle point problem with application to the elasticity imaging inverse problem.We examine three optimization formulations for the inverse problem, namely, the output least-squares (OLS), the modified output least-squares (MOLS), and the energy output least-squares (EOLS).The OLS functional and the EOLS functional are, in general, nonconvex; however, we show that the MOLS functional is convex.We provide existence results for optimization problems involving the regularized variants of the OLS, the EOLS, and the MOLS functional.We give first-order and second-order adjoint methods in the continuous setting to compute the first-order and the second-order derivative of the OLS/EOLS functionals.The derivative of the MOLS objective does not involve the derivative of the solution map and hence does not require the adjoint approach.We provide numerical experimentation on tissue phantom data.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".