Accelerating Thermal Homann Flow Simulation With Mesh-Based Graph Neural Networks
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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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) | 0.000 | 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 | 0.001 | 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".