Numerical upscaling of electrical conductivity: A problem specific approach to generate coarse-scale models
Bibliographic record
Abstract
In this work we propose a new approach for the upscaling problem of electrical conductivity in the context of electromagnetic methods. We pose the upscaling problem as a parameter estimation problem, which allow us to develop a goaloriented, quantitative framework that combines widely used simulation tools such as Mimetic Finite Volume, inversion and optimization techniques. We thus create a flexible methodology that allows the users to estimate, in an affordable manner, coarse-scale conductivity models that approximate, in some sense, the fine-scale ones. Our framework is based on the observation that for any conductivity model a number of different criteria can be considered for the homogenization problem. In particular, different physical fields and fluxes can be considered. Our framework allows the choice of the criteria that is the most appropriate for the goal of the simulation. Results are illustrated with a couple of simulations that demonstrate the capabilities of our method as well as the challenges that this different perspective offers.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 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".