Fast Direct Solution of 2D Scalar Volume Integral Equation via Tensor Train Decomposition for Scatterers of Arbitrary Shape
Bibliographic record
Abstract
The method of moments (MoM) discretization of the volume integral equation (VIE) is an effective tool for calculating field responses in the presence of arbitrary scatterers. This method scales poorly with problem size, however, due to the inherent difficulty of inverting the relevant matrix equations. The application of tensor train (TT) decomposition techniques has recently shown promise in alleviating the complexity of such calculations, with dramatic efficiency boosts in both computational time and memory having been proven possible for very simple scatterers. For arbitrary scatterers, previous work has shown that a conjugate gradient- TT (CG- TT) procedure was still capable of producing favorable runtime and memory complexities, particularly in quasi-constant rank regimes. In this work, we consider a direct solution of TT decomposed MoM matrix equation approach that is largely insensitive to MoM matrix condition number, while maintaining the generality of CG- TT. Preliminary results indicate that this approach is capable of matching the efficiency of CG- TT in the quasi-constant rank regime for scatterers of arbitrary geometry.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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) | 0.001 | 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 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".