Physics-informed neural networks with trainable sinusoidal activation functions for approximating the solutions of the Navier-Stokes equations
Bibliographic record
Abstract
We present TSA-PINN, a novel Physics-Informed Neural Network (PINN) that leverages a Trainable Sinusoidal Activation (TSA) mechanism to approximate solutions to the Navier-Stokes equations. By incorporating neuron-wise sinusoidal activation functions with trainable frequencies and a dynamic slope recovery mechanism, TSA-PINN achieves superior accuracy and convergence. Its ability to dynamically adjust activation frequencies enables efficient modeling of complex fluid behaviors, reducing training time and computational cost. Our testing goes beyond canonical problems, to study less-explored and more challenging scenarios, which have typically posed difficulties for prior models. Various numerical tests underscore the efficacy of the TSA-PINN model across five different scenarios. These include steady-state two-dimensional flows in a lid-driven cavity at two different Reynolds numbers; a cylinder wake problem characterized by oscillatory fluid behavior; and two time-dependent three-dimensional turbulent flow cases. In the turbulent cases, the focus is on detailed near-wall phenomena—including the viscous sub-layer, buffer layer, and log-law region—as well as the complex interactions among eddies of various scales. Both numerical and quantitative analyses demonstrate that TSA-PINN offers substantial improvements over conventional PINN models. This research advances physics-informed machine learning, setting a new benchmark for modeling dynamic systems in scientific computing and engineering.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 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".