A Study of Covariance Functions for Multi-Response Metamodeling for Simulation-Based Design and Optimization
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Bibliographic record
Abstract
The optimal design of complex systems in engineering requires the availability of mathematical models of system’s behavior as a function of a set of design variables; such models allow the designer to find the best solution to the design problem. However, system models (e.g. CFD analysis, physical prototypes) are usually time-consuming and expensive to evaluate, and thus unsuited for systematic use during design. Approximate models, or metamodels, of system behavior based on a limited set of data allow significant savings by reducing the resources devoted to modeling during the design process. In our work in engineering design based on multiple performance criteria, we propose the use of Multi-response Bayesian Surrogate Models (MRBSM) to model several aspects of system behavior jointly, instead of modeling each individually. By doing so, it is expected that the observed correlation among the response variables can be used to achieve better models with smaller data sets. In this work, we study the approximation capabilities of several covariance functions needed for multi-response metamodeling with MRBSM, performing a simulation study in which we compare MRBSM based on different covariance functions against metamodels built individually for each response. Our preliminary results indicate that MRBSM outperforms individual metamodels in 46% to 67% of the test cases, though the relative performance of the studied covariance functions is highly dependent on the sampling scheme used and the actual correlation among the observed response values.
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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 | 0.001 |
| 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