Computational techniques for solving the bidomain equations in three dimensions
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Bibliographic record
Abstract
The bidomain equations are the most complete description of cardiac electrical activity. Their numerical solution is, however, computationally demanding, especially in three dimensions, because of the fine temporal and spatial sampling required. This paper methodically examines computational performance when solving the bidomain equations. Several techniques to speed up this computation are examined in this paper. The first step was to recast the equations into a parabolic part and an elliptic part. The parabolic part was solved by either the finite-element method (FEM) or the interconnected cable model model (ICCM). The elliptic equation was solved by FEM on a coarser grid than the parabolic problem and at a reduced frequency. The performance of iterative and direct linear equation system solvers was analyzed as well as the scalability and parallelizability of each method. Results indicate that the ICCM was twice as fast as the FEM for solving the parabolic problem, but when the total problem was considered, this resulted in only a 20% decrease in computation time. The elliptic problem could be solved on a coarser grid at one-quarter of the frequency at which the parabolic problem was solved and still maintain reasonable accuracy. Direct methods were faster than iterative methods by at least 50% when a good estimate of the extracellular potential was required. Parallelization over four processors was efficient only when the model comprised at least 500,000 nodes. Thus, it was possible to speed up solution of the bidomain equations by an order of magnitude with a slight decrease in accuracy.
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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