Towards an hybrid computational strategy based on Deep Learning for incompressible flows
Bibliographic record
Abstract
The Poisson equation is present in very different domains of physics and engineering. In most cases, this equation can not be solved directly and iterative solvers are used. For many solvers, this step is computationally intensive. In this study, an alternative resolution method based on neural networks is evaluated for incompressible flows. A fluid solver coupled with a Convolutional Neural Network is developed and trained on random cases with constant density to predict the pressure field. Its performance is tested in a plume configuration, with different buoyancy forces, parametrized by the Richardson number. The neural network is compared to a traditional Jacobi solver. The performance improvement is considerable, although the accuracy of the network is found to depend on the flow operating point: low errors are obtained at low Richardson numbers, whereas the fluid solver becomes unstable with large errors for large Richardson number. Finally, a hybrid strategy is proposed in order to benefit from the calculation acceleration while ensuring a user-defined accuracy level. In particular, this hybrid CFD-NN strategy, by maintaining the desired accuracy whatever the flow condition, makes the code stable and reliable even at large Richardson numbers for which the network was not trained for. This study demonstrates the capability of the hybrid approach to tackle new flow physics, unseen during the network training.
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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) | 0.001 | 0.000 |
| 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".