Hybrid Physics-Informed Neural Network for the Wave Equation With Unconditionally Stable Time-Stepping
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Bibliographic record
Abstract
This letter introduces a novel physics-informed approach for neural network-based three-dimensional electromagnetic modeling. The proposed method combines standard leap-frog time-stepping with neural network-driven automatic differentiation for spatial derivative calculations in the wave equation. This methodology effectively addresses the challenge of accurately modeling high-frequency electromagnetic fields with physics-informed neural networks, often characterized as “spectral bias”, in the time domain. We demonstrate that the resultant numerical scheme enables unconstrained time-stepping with respect to stability, in contrast to the Finite-Difference Time-Domain method, which is subject to the Courant stability limit. Furthermore, the use of neural networks allows for seamless GPU acceleration. We rigorously evaluate the accuracy and efficiency of this finite-difference automatic differentiation approach, by comprehensive numerical experiments.
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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