Machine Learning in Fluid Dynamics—Physics-Informed Neural Networks (PINNs) Using Sparse Data: A Review
Bibliographic record
Abstract
Fluid mechanics often involves complex systems characterized by a large number of physical parameters, which are usually described by experimental and numerical sparse data (temporal or spatial). The difficulty of obtaining complete spatio-temporal datasets is a common issue with conventional approaches, such as computational fluid dynamics (CFDs) and various experimental methods, particularly when evaluating and modeling turbulent flows. This review paper focuses on the integration of machine learning (ML), specifically physics-informed neural networks (PINNs), as a means to address this challenge. By directly incorporating governing physical equations into neural network training, PINNs present a novel method that allows for the reconstruction of flow from sparse and noisy data. This review examines various applications in fluid mechanics where sparse data is a common problem and evaluates the effectiveness of PINNs in enhancing flow prediction accuracy. An overview of diverse PINNs methods, their applications, and outcomes is discussed, demonstrating their flexibility and effectiveness in addressing challenges related to sparse data and illustrating that the future of fluid mechanics lies in the synergy between data-driven approaches and established physical theories.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".