arXiv:2607. 05271v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) encounter ill-posed optimization, loss competition, and parameter compensation in partial differential equation (PDE) inverse problems.
By Qian Hu, Bin Fan, Yao Xiao, Zhicheng Lin, Meixin Xiong
arXiv:2509. 09513v3 Announce Type: replace-cross Abstract: Biophysical diffusion MRI models like Neurite Exchange Imaging (NEXI) are essential for probing gray matter microstructure, estimating compartment diffusivities, neurite fraction, and exchange time.
By Quentin Uhl, Tommaso Pavan, Julianna Gerold, Kwok-Shing Chan, Yohan Jun, Shohei Fujita, Aneri Bhatt, Yixin Ma, Qiaochu Wang, Hong-Hsi Lee, Susie Y. Huang, Berkin Bilgic, Ileana Jelescu
arXiv:2606. 02044v1 Announce Type: new Abstract: Diffusion MRI enables non-invasive probing of tissue microstructure, but accurate parameter estimation is challenged by noise-related effects.
By Bradley G. Karat, Ma\"eliss Jallais, Ali R. Khan, Santiago Aja-Fern\'andez, Jelle Veraart, Marco Palombo
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
Diffusion MRI enables non-invasive probing of tissue microstructure, but accurate parameter estimation is challenged by noise-related effects. In supervised machine learning frameworks trained on simulated data, discrepancies between the noise characteristics of simulated and acquired signals introduce a form of covariate shift, whereby the input signal distribution differs between training and inference.
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.