Tensor Train Acceleration of Method of Moments Solution of Volume Integral Equation on Structured and Unstructured Meshes
Bibliographic record
Abstract
Method of Moments (MoM) discretization of the Integral Equations (IEs) of electromagnetics results in dense matrix equation. Such matrix equations require prohibitively large computational resources when the number of basis functions used in discretization reaches hundreds of thousands and higher. Tensor Train (TT) decomposition of the MoM dense matrix equations has been recently proposed [1] to drastically reduce both the memory use for matrix storage and the CPU time required for its multiplication with a vector. Toeplitz matrix resulting from MoM discretization of Volume Integral Equation (VIE) can be represented as a multi-dimensional matrix and stored as a product of smaller dimensional matrices (tensors). Such product of smaller dimensional matrices, also known as the tensor train (TT), can reduce the matrix storage from O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) to O(logN) at low frequencies and O(NlogN) at high frequencies. The product of the matrix in the TT form with a vector can be computed in O(NlogN) operations. In order to accelerate MoM solution of practical scattering problems we recently developed Conjugate-Gradient-Tensor-Train (CG-TT) [2] and Precorrected-Tensor-Train (P-TT) [3] algorithms.
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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 | 0.000 | 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 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".