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.
arXiv:2607. 14193v1 Announce Type: cross Abstract: The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex.
By Boyuan Deng, Kshitiz Upadhyay, Michael Shields
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
By Lennon J. Shikhman
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
By Rajyasri Roy, Dibyajyoti Nayak, Somdatta Goswami
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
By Pierre Cesar (DATAMOVE), Sofya Dymchenko (DATAMOVE), Abhishek Purandare (DATAMOVE), Bruno Raffin (DATAMOVE)
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
By Yuanzhe Wang, Alexandre M. Tartakovsky
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
By Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University)
arXiv:2607. 24345v1 Announce Type: new Abstract: Neural spectral PDE solvers often learn an entire unresolved vector field even when an inexpensive approximate model can already capture most of the trajectory.
By Xianli Zhu, Jia Yin
arXiv:2509. 00203v3 Announce Type: replace Abstract: Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics.
By Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti