The Nested Superblock Approach for Regional‐Scale Analytic Element Models
Bibliographic record
Abstract
A new approach is presented for improving the computational efficiency of regional-scale ground water models based on the analytic element method (AEM). The algorithm is an extension of the existing "superblock" algorithm, which combines the effects of multiple analytic elements into Laurent series and Taylor series (superblock expansions). With the new "nested superblock" formulation, Laurent series are nested in a hierarchical (quad-tree) data structure with direct mathematical relationships between parent and child superblock coefficients. Nested superblocks significantly accelerate the evaluation of the complex potential and discharge function in models that contain a large number of analytic elements at multiple scales. This evaluation process, the primary computational cost of AEM models, is required to determine the element coefficients, generate contour plots, and trace pathlines. The performance of the nested superblocks is demonstrated with a simplified model based on the Lake Ontario watershed geometry comprising thousands of hydrogeologic features at multiple geographic scales.
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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 | 0.001 | 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".