An efficient algorithm for computing nearest medium approximations to an arbitrary anisotropic stiffness tensor
Bibliographic record
Abstract
ABSTRACT The problem of reducing a fully anisotropic (triclinic) stiffness tensor comprised of 21 distinct components to a higher symmetry form having fewer distinct elements is of interest in many geophysical applications, where assuming a particular type of symmetry is often necessary to sufficiently reduce computational complexity to allow practical solutions. In addition, recent advances in the upscaling of realistically large field-scale discrete fracture networks have led to the need for an efficient way to derive a very large number of nearest medium approximations to the triclinic stiffness tensors obtained. Owing to rotational symmetries and nonlinearity, the problem of efficiently finding such approximations is generally nontrivial because optimal orientations are intrinsically nonunique. An algorithm proposed by Dellinger computes nearest orthotropic and transverse isotropic approximations for a given stiffness tensor, using the Federov norm as an objective function to iteratively minimize the fit error. Although this method is appropriate for computing solutions to single problem instances, the implementation is too inefficient for production situations, where a very large number of invocations of the algorithm is required. The enhanced algorithm proposed here is accurate, efficient, and general, allowing nearest medium approximations to be determined for arbitrary symmetry types, including isotropic, cubic, transverse isotropic, orthotropic, and monoclinic.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".