arXiv:2606. 03936v1 Announce Type: new Abstract: Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters.
By Niccol\`o Perrone, Fanny Lehmann, Stefania Fresca, Filippo Gatti
Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain.
Magnetic resonance imaging (MRI) super-resolution is vital for improving diagnostic accessibility, yet most methods treat it as a deterministic mapping from a fixed low-resolution input to a high-resolution target. This overlooks a key property of MRI acquisition physics: spatial resolution and signal-to-noise ratio (SNR) are inherently coupled, making any given low-resolution scan merely one of many possible realizations under varying acquisition trade-offs.
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.
By Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask
arXiv:2607. 04407v1 Announce Type: cross Abstract: Repeated prediction of acoustic fields from spatially distributed boundary excitation is computationally expensive when each source realization requires a new wave simulation.
By Muhammad Idrees Khan, Hua-Dong Yao
arXiv:2508. 20650v2 Announce Type: replace Abstract: Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framework.
By Juncai He, Xinliang Liu, Jinchao Xu