arXiv:2609.35938v1 Announce Type: new
Abstract: This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitl...
By Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu
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:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.
By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma
arXiv:2607. 27062v1 Announce Type: cross Abstract: Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models.
By Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria, Lorenzo Rosasco
The paper proposes Domain-aware Fourier Features (DaFFs) for Physics-Informed Neural Networks (PINNs), embedding domain-specific geometry and boundary conditions into the positional encoding. DaFFs eliminate the need for explicit boundary loss terms, simplify optimization, and reduce training cost, leading to orders-of-magnitude lower errors and faster convergence compared to vanilla PINNs and RFF-based PINNs. An LRP-based explainability framework further shows that DaFFs produce more physically consistent relevance attributions, improving interpretability.
By Alberto Mi\~no Calero, Luis Salamanca, Konstantinos E. Tatsis
Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.