Error Metrics and the Sequential Refinement of Kriging Metamodels
Bibliographic record
Abstract
Metamodels, or surrogate models, have been proposed in the literature to reduce the resources (time/cost) invested in the design and optimization of engineering systems whose behavior is modeled using complex computer codes, in an area commonly known as simulation-based design optimization. Following the seminal paper of Sacks et al. (1989, “Design and Analysis of Computer Experiments,” Stat. Sci., 4(4), pp. 409–435), researchers have developed the field of design and analysis of computer experiments (DACE), focusing on different aspects of the problem such as experimental design, approximation methods, model fitting, model validation, and metamodeling-based optimization methods. Among these, model validation remains a key issue, as the reliability and trustworthiness of the results depend greatly on the quality of approximation of the metamodel. Typically, model validation involves calculating prediction errors of the metamodel using a data set different from the one used to build the model. Due to the high cost associated with computer experiments with simulation codes, validation approaches that do not require additional data points (samples) are preferable. However, it is documented that methods based on resampling, e.g., cross validation (CV), can exhibit oscillatory behavior during sequential/adaptive sampling and model refinement, thus making it difficult to quantify the approximation capabilities of the metamodels and/or to define rational stopping criteria for the metamodel refinement process. In this work, we present the results of a simulation experiment conducted to study the evolution of several error metrics during sequential model refinement, to estimate prediction errors, and to define proper stopping criteria without requiring additional samples beyond those used to build the metamodels. Our results show that it is possible to accurately estimate the predictive performance of Kriging metamodels without additional samples, and that leave-one-out CV errors perform poorly in this context. Based on our findings, we propose guidelines for choosing the sample size of computer experiments that use sequential/adaptive model refinement paradigm. We also propose a stopping criterion for sequential model refinement that does not require additional samples.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.015 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| 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".