Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, Isomap and kernel Isomap are used to dramatically reduce the dimensionality of the output space to efficiently construct a Gaussian process emulator of parametrized partial differential equations. The output space consists of spatial or spatio-temporal fields that are functions of multiple input variables. For such problems, standard multi-output Gaussian process emulation strategies are computationally impractical and/or make restrictive assumptions regarding the correlation structure. The method we develop can be applied without modification to any problem involving vector-valued targets and vector-valued inputs. It also extends a method based on linear dimensionality reduction to response surfaces that cannot be described accurately by a linear subspace of the high dimensional output space. Comparisons to the linear method are made through examples that clearly demonstrate the advantages of nonlinear dimensionality reduction.
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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 | 0.001 |
| 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