Tensor-Train Accelerated Solution of 3D Vector Volume Integral Equation Solutions with logN Complexity
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Bibliographic record
Abstract
This study investigates the application of tensor train decomposition to model the matrix, excitation, and solution vectors of the dense matrix equation derived from the Method of Moments (MoM) discretization of the full-wave 3D Volume Integral Equation. These components are represented as a product of O(log(N)) small matrices (tensors). This quantized tensor train (QTT) decomposition demonstrates O(log(N)) efficiency in both CPU time and memory usage. To solve the matrix equation based on the QTT-represented system of linear algebraic equations (SLAE) with matrices and vectors, we implement an iterative GMRES scheme, which enables rapid matrix-vector product evaluations with O(log(N)) CPU time and memory requirements. Currently, this O(log(N)) performance applies only to SLAEs with purely Toeplitz matrices, particularly in scattering problems involving homogeneous dielectric scatterers made of cubic voxels.
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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) | 0.001 | 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 it