Accelerating Thermal Homann Flow Simulation With Mesh-Based Graph Neural Networks
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Bibliographic record
Abstract
The numerical simulation of Homann flow, a classical problem in fluid dynamics involving axisymmetric flow over a solid plate, is essential for understanding various boundary layer phenomena. Due to the prominence of this flow and its computationally intensive nature when dealing with complex geometries, the present paper explores the use of machine learning (ML) to solve Homann flow with heat transfer both rapidly and accurately. However, the application of ML, especially deep learning (DL), to engineering-focused physics simulations remains a significant challenge. Traditional numerical approaches have consistently demonstrated higher accuracy in simulation tasks compared to DL models, which often suffer from a lack of generalizability when predicting outcomes for geometries that differ slightly from those used in training. In this study, Graph Neural Networks (GNNs) are employed to solve thermal Homann flow on substrates of various geometries. We demonstrate that the trained model accurately predicts outcomes even on entirely novel cases, and notably, the computational efficiency of the GNN model significantly surpasses that of conventional numerical solvers.
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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