arXiv:2606. 18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN).
By Shayan Dodge (DESTeC, University of Pisa, Pisa, Italy), Alessandro Formisano (Department of Engineering, University of Campania Luigi Vanvitelli, Aversa, Italy), Sami Barmada (DESTeC, University of Pisa, Pisa, Italy)
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
By Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang, Peilin Zhan, Jianmin Lv, Jane You, C. L. Philip Chen
arXiv:2607. 03682v1 Announce Type: cross Abstract: Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized.
By Zihao Guo, Xin Li, Zhihong Xia
arXiv:2606. 31342v1 Announce Type: cross Abstract: Partial differential equations on unbounded domains are challenging because the exterior region must be represented without excessive truncation error.
By Haixin Wang, Haoning Dang, Fei Wang, Shimin Guo
arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.
By Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati, Saeid Gorgin
arXiv:2608. 08114v1 Announce Type: cross Abstract: In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs).
By Jeeeun Lee, Denis Korolev, Miro Duhovic, Seong Su Kim