arXiv:2606. 05199v1 Announce Type: cross Abstract: The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters.
By Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka
arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.
By Zhen Zhang, Alessandro Alla, George Em Karniadakis
arXiv:2502. 00803v3 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function.
By Yuezhou Ma, Haixu Wu, Hang Zhou, Huikun Weng, Jianmin Wang, Mingsheng Long
arXiv:2608. 16475v1 Announce Type: cross Abstract: The Porous Medium Equation (PME), given by $u_t = \Delta(u^m)$ for $m > 1$, is a degenerate nonlinear parabolic partial differential equation that arises in various physical applications such as fluid flow in porous media, heat transfer in plasmas, and population dynamics.
By Noura Al Helwani, Sophie Moufawad, Nabil Nassif
arXiv:2606. 06313v1 Announce Type: cross Abstract: Wall shear stress (WSS) governs near-wall transport dynamics and is a key hemodynamic indicator in cardiovascular flows, yet remains difficult to infer accurately due to the need for precise computation of near-wall velocity gradients.
By Mahmoud Elhadidy, Siva Viknesh, Roshan M. D'Souza, Amirhossein Arzani
arXiv:2606. 02475v1 Announce Type: cross Abstract: Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed.
By Henry Kasumba, Ronald Katende