The Development of Physical Informed Neural Networks for Fluid Flow in Infinite Parallel Plates As Compared to CFD and AI Models
Bibliographic record
Abstract
Abstract In this study, we developed neural network models from two different perspectives; Artificial Neural Networks (ANNs) and Physics Informed Neural Networks (PINNs) to model fluid flow in infinite parallel plates under laminar flow conditions. The ANNs model compared with the theoretical solution, while the PINNs model evaluated against a Computational Fluid Dynamics (CFD) model. The ANNs model predicts the non-dimensional pressure gradient in fully developed flow between infinite parallel plates. A significant limitation lies in its requirement for extensive data, posing a considerable challenge in practical scenarios. Similar to ANNs model; PINNs model is also mesh-free, applicable to any shape, and does not require a deep understanding of physical phenomena. However, Unlike the ANNs model, the PINNs model does not require extensive data. Despite these advantages interpreting the learned parameters or hidden representations within PINNs is challenging. In contrast, the CFD model, specifically the control volume approach within the SIMPLE algorithm, provides a clear physical interpretation of the numerical solution of fluid flow problems. However, it is affected by grid dependency, highly sensitive to boundary conditions, and it is also mathematically complicated. This comprehensive analysis and comparison provide valuable theoretical and fundamental insights for interdisciplinary researchers in the field, addressing fluid dynamics challenges and offering step by step guideline for implementation of Neural Networks models to solve fluid dynamics problems.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 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".