Solving the Helmholtz and Electro-Thermal Coupling Equations Using Physics-Informed GNNs
Bibliographic record
Abstract
Building on the graph-neural network architecture proposed by Hao Zhang et al., we propose a novel physicsinformed neural network (PINN) approach for efficiently solving both the Helmholtz equation and a coupled electro-thermal problem in two dimensions. By viewing the computational mesh as a graph, we employ an encoder-processor-decoder architecture that learns local interactions among mesh nodes while enforcing the underlying physical laws through PDE-informed loss terms. The novelty of this approach lies in leveraging graph neural networks (GNNs) to incorporate prior and geometric domain information for accurate and scalable numerical computation of electromagnetic and thermal fields. Numerical experiments confirm the model's ability to replicate the known solution with high accuracy, suggesting that this Physics-Informed Graph Neural Network (PIGNN) can be employed as a surrogate model for fast solutions to electromagnetic and multi-physics problems for which traditional methods require more time.
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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 | 0.001 |
| 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".