A generalized framework for unsupervised learning and data recovery in computational fluid dynamics using discretized loss functions
Bibliographic record
Abstract
The authors present generalized finite-volume-based discretized loss functions integrated into pressure-linked algorithms for physics-based unsupervised training of neural networks (NNs). In contrast to automatic differentiation-based counterparts, discretized loss functions leverage well-developed numerical schemes of computational fluid dynamics (CFD) for tailoring NN training specific to the flow problems. For validation, neural network-based solvers (NN solvers) are trained by posing equations such as the Poisson equation, energy equation, and Spalart–Allmaras model as loss functions. The predictions from the trained NNs agree well with the solutions from CFD solvers while also providing solution time speed-ups of up to seven times. Another application of unsupervised learning is the novel hybrid loss functions presented in this study. Hybrid learning combines the information from sparse or partial observations with a physics-based loss to train the NNs accurately and provides training speed-ups of up to five times compared with a fully unsupervised method. Also, to properly utilize the potential of discretized loss functions, they are formulated in a machine learning (ML) framework (TensorFlow) integrated with a CFD solver (OpenFOAM). The ML-CFD framework created here infuses versatility into the training by giving loss functions access to the different numerical schemes of the OpenFOAM. In addition, this integration allows for offloading the CFD programming to OpenFOAM, circumventing bottlenecks from manually coding new flow conditions in a solely ML-based framework like TensorFlow.
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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 | 0.004 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".