Data completion and stochastic algorithms for PDE inversion problems\n with many measurements
Why this work is in the frame
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Bibliographic record
Abstract
Inverse problems involving systems of partial differential equations (PDEs)\nwith many measurements or experiments can be very expensive to solve\nnumerically. In a recent paper we examined dimensionality reduction methods,\nboth stochastic and deterministic, to reduce this computational burden,\nassuming that all experiments share the same set of receivers. In the present\narticle we consider the more general and practically important case where\nreceivers are not shared across experiments. We propose a data completion\napproach to alleviate this problem. This is done by means of an approximation\nusing an appropriately restricted gradient or Laplacian regularization,\nextending existing data for each experiment to the union of all receiver\nlocations. Results using the method of simultaneous sources (SS) with the\ncompleted data are then compared to those obtained by a more general but slower\nrandom subset (RS) method which requires no modifications.\n
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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