arXiv Machine Learning By Devesh Shah

Complementary, Not Cumulative: Interaction Effects in Physics-Informed Neural Networks for Navier-Stokes Vortex Shedding

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arXiv:2608. 19632v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) embed governing partial differential equations directly into the training loss, offering a promising alternative to costly CFD solvers for unsteady flows.

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arXiv Machine Learning
Jul 15

MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries

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
arXiv Machine Learning
Aug 31

Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems

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 Machine Learning
Aug 17

Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets

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