Uncertainty analysis of effective elasticity tensors using quaternion-based global optimization and Monte-Carlo method
Bibliographic record
Abstract
We consider the problem of representing a generally anisotropic elasticity tensor, which might be obtained from physical measurements, by a tensor belonging to a chosen material symmetry class, so-called ‘effective tensor'. Following previous works on the subject, we define this effective tensor as the solution of a global optimization problem for the Frobenius distance function. For all nontrivial symmetry classes, except isotropy, this problem is nonlinear, since it involves all orientations of the symmetry groups. We solve the problem using a metaheuristic method called particle-swarm optimization and employ quaternions to parametrize rotations in 3-space to improve computational efficiency. One advantage of this approach over previously used plot-guided local methods and exhaustive grid searches is that it allows us to solve a large number of instances of the problem in a reasonable time. As an application, we can use Monte-Carlo method to analyze the uncertainty of the orientation and elasticity parameters of the effective tensor resulting from the uncertainty of the given tensor, which may be caused, for example, by measurement errors.
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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 | 0.004 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".