Sensitivity-based Adaptive Sampling for Physics-Informed Neural Networks
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Bibliographic record
Abstract
For training the Physics-Informed Neural Networks (PINNs), the allocation of collocation points in the geometric domain plays a pivotal role in determining the model’s performance. We present a novel sampling method tailored for optimal point allocation in PINNs. The method involves an initial meshing of the domain, followed by a calculation of the sensitivity matrix relating the losses for each mesh element to local changes in the locations of the training points. Subsequently, based on the principles of A-optimal experimental design, the sampling probability is dynamically redistributed over the domain. In this way, areas of high sensitivity and corresponding physical significance receive further representation in the training data. Preliminary results illustrate the effectiveness of the proposed method when applied to the problem of developing flow between two parallel plates. This sensitivity-based sampling (SBS) is shown to increase the overall precision of PINNs since it can specifically capture sharp gradients in critical points within the geometric domain.
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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