arXiv:2607. 11094v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy.
By Zhangyi Lian, Xinda Dong, Wenxuan Huo, Weifeng Huang, Gang Zhu, Qiang He
arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).
By Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar
arXiv:2606. 20442v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training.
By Fedor Buzaev (HSE University), Dmitry Efremenko (HSE University), Egor Bugaev (HSE University), Andrei Ermakov (HSE University, AXXX), Denis Derkach (HSE University), Daria Pugacheva (HSE University, AXXX), Fedor Ratnikov (HSE University)
arXiv:2605. 25001v2 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology.
By Yichen Luo, Peiyu Zhu, Dongxiao Hu, Jia Wang, Tailin Wu, Dapeng Lan, Yu Liu, Zhibo Pang
arXiv:2608. 04778v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets.
By Xujia Chen, Xinyue Hu, Letian Chen, Yi Liu, Wenhui Fan
arXiv:2608. 16930v1 Announce Type: cross Abstract: Existing multi-task learning methods rely on hard sharing, multiple paths or experts, adaptive sharing, and dynamic expansion.
By Chenlei Fang, Jingchen Li, Hongzong LI, Qingyao Li, Yixuan Zhang, Huarui Wu, Haobin Shi, Chunjiang Zhao
arXiv:2607. 26490v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics.
By Peng Yin, Kai Li, Yifan Zhang, Jian Cheng
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
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.
arXiv:2606. 25151v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) embed governing equations in their loss function, enabling mesh-free solutions to partial differential equations.
By David McShannon, Nicholas Dietrich
Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions. We show these failures are multi-causal, arising from the concurrent interplay of (i) spectral bias against sharp features, (ii) imbalanced multi-term optimization and loss-weight collapse, (iii) violation of temporal causality, and (iv) under-resolved collocation.
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