arXiv:2605. 25413v3 Announce Type: replace-cross Abstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs).
By Jiaquan Zhang, Caiyan Qin, Haoyu Bian, Libin Cai, Yi Lu, Chaoning Zhang, Wei Dong, Yuanfang Guo, Yang Yang, Heng Tao Shen
arXiv:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.
By Kuilin Qin, Lianfang Wang, Xu Sun, Jiwei Jia, Yu Wang, Yong Wang, Yuping Duan
arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.
By Mostafa Bamdad, Mohammad Sadegh Eshaghi, Timon Rabczuk
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
By Lennon J. Shikhman
arXiv:2607. 24345v1 Announce Type: new Abstract: Neural spectral PDE solvers often learn an entire unresolved vector field even when an inexpensive approximate model can already capture most of the trajectory.
By Xianli Zhu, Jia Yin
arXiv:2606. 16900v1 Announce Type: new Abstract: Physical systems often exhibit heterogeneous mechanisms, where rapidly evolving dynamics coexist with persistent structures.
By Hao Tang, Yuechen Duan, Jiongyu Zhu, Zimeng Feng, Hao Li, Chao Li