arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.
By Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati, Saeid Gorgin
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
arXiv:2606. 06171v1 Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions.
By Cornelius Otchere, Michael Shields
arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.
By Adrien Weihs, Chunyang Liao, Jingmin Sun, Hayden Schaeffer
arXiv:2604. 06001v2 Announce Type: replace-cross Abstract: Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems.
By Xiaolong Wang, Jing Feng, Qi Liu, Chengli Tan, Yuanyuan Liu, Yong Xu
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou