Physics-Informed Deep Operator Network for 3-D Time-Domain Electromagnetic Modeling
Bibliographic record
Abstract
This article presents a modeling technique for realistic 3-D electromagnetic problems in the time domain, using a novel physics-informed deep operator network (PI-DON). The training of the PI-DON is executed in two stages. In the first stage, a neural operator is trained to approximate the curl operator in Maxwell’s equations. In the second stage, the neural curl operator is deployed with problem-specific settings to model electromagnetic fields through an unsupervised training approach, utilizing a physics-informed loss function. This unsupervised training eliminates the need to generate ground-truth data and reduces the volume of training data required, making PI-DON more efficient than traditional deep neural networks. As an electromagnetic solver, PI-DON demonstrates competitive efficiency compared to finite-difference time-domain (FDTD) solvers for a single run, even when accounting for its training time. Moreover, PI-DON shows strong generalizability, allowing for accurate and efficient uncertainty quantification and design optimization of microwave geometries without additional training. We show the high accuracy, efficiency, and robust generalizability of the PI-DON solver through the modeling and uncertainty quantification of 3-D planar microwave circuits and a metasurface unit cell.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".