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
The paper introduces Sensitivity‑Constrained Neural Operators (SC‑NOs), which augment standard neural operator training with sampled Jacobian supervision from differentiable solvers or discrete adjoints. By matching selected sensitivities during training, SC‑NOs improve forward prediction accuracy and significantly enhance gradient‑based inverse reconstruction for distributed fields. Experiments on advection–diffusion, RANS–Spalart–Allmaras, high‑dimensional gridded inputs, and a shallow‑water tsunami source‑inversion case demonstrate that SC‑NOs achieve a better accuracy–cost trade‑off and enable near‑real‑time wave‑propagation forecasting from sparse observations.
By Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer, Kathryn Lawson
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)