analiza aiqbench
This research advances Physics-Informed Neural Networks (PINNs) by introducing an adaptive training framework that significantly improves accuracy in solving the Blasius boundary-layer equation. By combining gradient-norm-based loss weighting with nonuniform collocation and sequential optimization, the method reduces wall-shear error by over 20 times compared to prior PINN implementations. The study highlights that optimizing loss functions alone is insufficient for achieving high physical fidelity, necessitating a holistic approach to training strategies in scientific machine learning.
Adaptive Physics-Informed Neural Networks for the Blasius Boundary-Layer Problem
arXiv:2609.22185v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) provide a mesh-free approach for solving differential equations, but their performance can depend strongly on loss weighting, collocation placement, and optimization strategy. This study develops an adaptive PINN framework for the Blasius boundary-layer equation using gradient-norm-based adaptive loss weighting, nonuniform and residual-based collocation, and sequential Adam--L-BFGS optimization. In the representative run using the architecture $[1,100,100,1]$, the model predicts $f''(0)=0.3320762918$, compared with the high-accuracy benchmark $0.332057336215$, giving an absolute error of $1.896\times10^{-5}$. The final weighted loss is $6.789\times10^{-8}$, and the predicted stream-function, velocity, and shear profiles agree closely with an independent numerical boundary-value solution. A separate full-training architecture study shows that the two-hidden-layer model achieves the smallest wall-shear error among the four tested architectures, $1.629\times10^{-6}$, whereas the deepest network attains the smallest weighted objective but a substantially larger wall-shear error. Compared with the previously reported PINN value $f''(0)=0.33165$, the representative run reduces the wall-shear error by approximately a factor of $21.5$. The results show that the combined adaptive training framework can achieve high accuracy for the Blasius problem and that weighted loss alone is insufficient for identifying the most physically accurate PINN. Because the adaptive components are applied jointly, their individual contributions cannot be isolated from the present results and would require a controlled ablation study for separate assessment.
Abstract:Physics-informed neural networks (PINNs) provide a mesh-free approach for solving differential equations, but their performance can depend strongly on loss weighting, collocation placement, and optimization strategy. This study develops an adaptive PINN framework for the Blasius boundary-layer equation using gradient-norm-based adaptive loss weighting, nonuniform and residual-based collocation, and sequential Adam--L-BFGS optimization. In the representative run using the architecture $[1,100,100,1]$, the model predicts $f''(0)=0.3320762918$, compared with the high-accuracy benchmark $0.332057336215$, giving an absolute error of $1.896\times10^{-5}$. The final weighted loss is $6.789\times10^{-8}$, and the predicted stream-function, velocity, and shear profiles agree closely with an independent numerical boundary-value solution. A separate full-training architecture study shows that the two-hidden-layer model achieves the smallest wall-shear error among the four tested architectures, $1.629\times10^{-6}$, whereas the deepest network attains the smallest weighted objective but a substantially larger wall-shear error. Compared with the previously reported PINN value $f''(0)=0.33165$, the representative run reduces the wall-shear error by approximately a factor of $21.5$. The results show that the combined adaptive training framework can achieve high accuracy for the Blasius problem and that weighted loss alone is insufficient for identifying the most physically accurate PINN. Because the adaptive components are applied jointly, their individual contributions cannot be isolated from the present results and would require a controlled ablation study for separate assessment.
Machine Learning (cs.LG); Fluid Dynamics (physics.flu-dyn)
arXiv:2609.22185 [cs.LG]
(or arXiv:2609.22185v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.22185 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 309 cuvinte
Subiecte conexe
Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach
arXiv · 4 sept. 2026
The J-Space Debate, Agent Swarms, and Pacing Frontier AI - Digital Minds Newsletter #4
LessWrong · 18 sept. 2026
Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution
arXiv · 15 sept. 2026
An Adaptive Machine Learning Framework for Fluid Flow in Dual-Network Porous Media
arXiv · 24 sept. 2026