On the scalability of truss geometry and topology optimization with global stability constraints via chordal decomposition
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Bibliographic record
Abstract
Abstract Geometry optimization was recently introduced to existing truss topology optimization with global stability constraints. The resulting problems are formulated as highly nonlinear semidefinite programming problems that demand extensive computational effort to solve and have been solved only for small problem instances. The main challenge for effective computation is the positive semidefinite constraints which involve large sparse matrices. In this paper, we apply several techniques to tackle the challenge. First, we use the well-known chordal decomposition approach to replace each positive semidefinite constraint on a large sparse matrix by several positive semidefinite constraints on smaller submatrices together with suitable linking constraints. Moreover, we further improve the efficiency of the decomposition by applying a graph-based clique merging strategy to combine submatrices with significant overlap. Next, we couple these techniques with an optimization algorithm that fully exploits the structure of the smaller submatrices. As a result, we can solve much larger problems, which allows us to extend the existing single-load case to the multiple-load case, and to provide a computationally tractable approach for the latter case. Finally, we employ adaptive strategies from previous studies to solve successive problem instances, enabling the joints to navigate larger regions, and ultimately obtain further improved designs. The efficiency of the overall approach is demonstrated via computational experiments on large problem instances.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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