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:2608. 05892v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems.
By Yulun Wu, Matthieu Barreau, Miguel Aguiar, Karl H. Johansson
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi
arXiv:2510. 10350v3 Announce Type: replace-cross Abstract: Operator learning provides a data-driven approach to approximating solution operators of partial differential equations, but its effectiveness depends strongly on how input and output functions are represented.
By Chuqi Chen, Yang Xiang, Weihong Zhang
arXiv:2607. 25608v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks.
By Pinki Khatun, M. Sajid, Abhinav Jha, M. Tanveer
Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems. Two factors underlie this difficulty: spectral bias, the tendency of neural networks to underfit high-frequency features; and representation-coefficient coupling, the entanglement of representation learning and coefficient fitting within a single nonconvex optimization objective.