Large-scale magnetic inversion using differential equations and ocTrees
Bibliographic record
Abstract
The inversion of large-scale magnetic data sets has historically been successfully achieved through integral transforms of the large, dense sensitivity matrix. Two well-known transforms, the discrete Fourier and multi- dimensional wavelet, reduce the required storage and ultimately speed of the inversion by storing only the necessary transform coefficients without losing accuracy. The main drawback of the approaches is the required calculation of the entire dense sensitivity matrix prior to the transform. This process can be much more costly than the inversion itself. We solve the magnetostatic Maxwell’s equation using a finite volume technique on an ocTree-based mesh. The ocTree mesh greatly reduces the time required for the inversion process. When working in the differential equation domain it is not necessary to explicitly form the sensitivity matrix; this decreases the storage requirement of the problem and increases the overall speed of the inversion. The principal mesh is broken up into sub-domain ocTree grids to further enable parallelization of the forward problem. These grids extend the entire domain of the principal mesh to include large regional features that may influence the data. We present the discretization of the equations and verify the accuracy of the modelling both with the principal mesh and with multiple sub-domains. We show a synthetic example and a large field example consisting of over 4 million data and 5 million model cells that was inverted on a desktop computer.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".