Deep Neural Network Modeling for CFD Simulations: Benchmarking the Fourier Neural Operator on the Lid-Driven Cavity Case
Bibliographic record
Abstract
In this work we present the development, testing and comparison of three different physics-informed deep learning paradigms, namely the ConvLSTM, CNN-LSTM and a novel Fourier Neural Operator (FNO), for solving the partial differential equations of the RANS turbulence model. The 2D lid-driven cavity flow was chosen as our system of interest, and a dataset was generated using OpenFOAM. For this task, the models underwent hyperparameter optimization, prior to testing the effects of embedding physical information on performance. We used the mass conservation of the model solution, embedded as a term in our loss penalty, as our physical information. This approach has been shown to give physical coherence to the model results. Based on the performance, the ConvLSTM and FNO models were assessed in forecasting the flow for various combinations of input and output timestep sizes. The FNO model trained to forecast one timestep from one input timestep performed the best, with an RMSE for the overall x and y velocity components of 0.0060743 m·s−1.
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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 | 0.001 | 0.003 |
| 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) | 0.001 | 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".