A Global High Dimensional Metamodeling Approach With the Ability of Using Non-Uniform Sampling
Bibliographic record
Abstract
In engineering design, spending excessive amount of time on physical experiments or expensive simulations makes the design costly and lengthy. This issue exacerbates when the design problem has a large number of inputs, or of high dimension. High Dimensional Model Representation (HDMR) is one powerful method in approximating high dimensional, expensive, black-box (HEB) problems. One existing HDMR implementation, Random Sampling HDMR (RS-HDMR), can build a HDMR model from random sample points with a linear combination of basis functions. The most critical issue in RS-HDMR is that calculating the coefficients for the basis functions includes integrals that are approximated by Monte Carlo summations, which are error prone with limited samples and especially with non-uniform sampling. In this paper, a new approach based on Principal Component Analysis (PCA), called PCA-HDMR, is proposed for finding the coefficients that provide the best linear combination of the bases with minimum error and without using any integral. Benchmark problems are modeled using the method and the results are compared with RS-HDMR results. With both uniform and non-uniform sampling, PCA-HDMR built more accurate models than RS-HDMR for a given set of sample points.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".