Simulation of 3D turbulent flows using a discretized generative model physics-informed neural networks
Bibliographic record
Abstract
Physics-informed neural networks (PINNs) demonstrated efficacy in approximating partial differential equations (PDEs). However, challenges arise when dealing with high-dimensional PDEs, particularly when characterized by nonlinear and chaotic behavior, such as turbulent fluid flows. We introduce a novel methodology that integrates domain discretization , a generative model in the Sobolev function space ( H 1 ), and a gating mechanism to effectively simulate high dimensional problems. The effectiveness of the method, Discretized Generative Model Physics-Informed Neural Networks (DG-PINN), is validated by its application to the simulation of a time-dependent 3D turbulent channel flow governed by the incompressible Navier–Stokes equations, a less explored problem in the existing literature. Domain discretization prevents error propagation by using different neural network models in different subdomains . The absence of initial conditions (IC) in subsequent time steps presents a challenge in identifying optimal network parameters. To address this, discretized generative models are used, improving the model’s overall performance. The global solutions’ regularity is enhanced compared to previous decomposition techniques by using the H 1 norm of error, rather than L 2 . The effectiveness of the DG-PINN is validated through numerical test cases and compared against baseline PINNs and traditional domain decomposition PINNs. The DG-PINN demonstrates improvement in both approximation accuracy and computational efficiency, consistently maintaining accuracy even at later time instances. Moreover, the implementation of a distributed training strategy, facilitated by domain discretization, is discussed, resulting in improved convergence rates and more optimized memory usage.
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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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".