Proper generalized decomposition surrogate modeling with application to the identification of Rayleigh damping parameters
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Bibliographic record
Abstract
This paper extends the Proper Generalized Decomposition framework to develop a reduced-order model parameterized by Rayleigh damping coefficients. The developed method incorporates damping modes to construct a damped surrogate model effectively. A novel method is introduced for treating the problem in space: during the offline phase, the spatial problem is initially projected onto the subspace spanned by the Ritz vectors of the system to provide an efficient prediction of the spatial modes. The prediction is then refined using a MinRes iterative solver. This two-step, prediction–correction process reduces the computational cost of a full-order solution while improving the accuracy of the reduced model. The resulting Proper Generalized Decomposition surrogate is subsequently employed within a Particle Swarm Optimization algorithm to determine optimal damping coefficients based on a given snapshot. Numerical experiments demonstrate the effectiveness of the developed method. • Low-rank representations of the damped parameterized equation for 3D elastodynamics. • Enhanced performance of the spatial solver by a new prediction–correction strategy. • Damping identification using the surrogate model and Particle Swarm Optimization. • Scalable method for accurate simulations of 3D viscoelastic structures.
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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 | 0.000 |
| 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