arXiv:2603. 08465v3 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving fluid-flow PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces (TPMS).
By Weizheng Zhang, Xunjie Xie, Hao Pan, Xiaowei Duan, Bingteng Sun, Qiang Du, Lin Lu
The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.
By Aleksandra Jekic, Afroditi Natsaridou, Signe Riemer-S{\o}rensen, Helge Langseth, Odd Erik Gundersen
arXiv:2609.06660v1 Announce Type: cross
Abstract: Accurate aerodynamic prediction is critical for designing fuel-efficient and safe transportation systems such as aircraft and automobiles, yet tradit...
By Wenxuan Jin, Jianguo Yao, Haibing Guan, Xijun Li
arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).
By Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
By Joseph Webb, Sadok Jerad, Coralia Cartis
arXiv:2608. 13629v1 Announce Type: cross Abstract: Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA).
By Oscar L. Cruz-Gonzalez, Val\'erie Deplano, Badih Ghattas