The residual velocity method applied to a steady free boundary-value problem of vector Laplacian type
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Bibliographic record
Abstract
We consider a free boundary-value problem based on a simplified model of two-phase flow in porous media. The model has two independent variables on each side of the free interface. At the interface at steady state, five mixed Dirichlet and Neumann conditions are given. The movement of the interface in time-dependent situations can be reduced to a normal motion proportional to the residual in one of the steady-state interface conditions (the elliptic interior problems and the other interface conditions are satisfied at each time). Following previous work, we consider the use of other residuals for the normal velocity that have superior numerical properties. The well-posedness criteria for this vector example are particularly clear. The advantages of the correctly chosen, non-physical residual velocities are demonstrated in numerical computations. Although the finite-difference implementation in this work is not applicable to general problems, it has superior performance to previous implementations.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 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