Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.
arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.
By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma
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:2606. 09923v1 Announce Type: cross Abstract: Neural operators such as the Fourier Neural Operator (FNO) have emerged as powerful surrogates for solving partial differential equations (PDEs), achieving speedups of several orders of magnitude over traditional numerical solvers.
By Michael Chin
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:2608.24049v1 Announce Type: new
Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
By Jihao Zhang, Junyi Guo, Jian-Xun Wang
The paper introduces StablePDENet, a physics-informed adversarial training framework that regularizes the residual sensitivity of neural operators to improve stability against input perturbations. The method formulates operator learning as a min–max optimization, where a physics-based projected‑gradient adversary generates perturbations and the outer objective combines the attacked physics loss with a normalized residual‑sensitivity penalty. Experiments on benchmark problems show that StablePDENet outperforms PI‑DeepONet and its adversarial variant in accuracy under adversarial attacks while maintaining competitive performance on clean data, and it also enhances generalization and highlights the distinction between model sensitivity and intrinsic operator ill‑conditioning.
By Chutian Huang, Chang Ma, Kaibo Wang, Yang Xiang
The paper introduces PAM-GS, a physics-aware gradient surgery technique for Physics-Informed Neural Networks (PINNs). It addresses the highly imbalanced multi-task optimisation problem in PINNs by adaptively mitigating task interference based on observed gradient conflicts. Experiments on four PDE benchmarks show that PAM-GS achieves competitive solution accuracy while maintaining strong task-balanced performance, outperforming existing methods on most problems.
By Thomas Borsani, Giuseppe Di Fatta
The paper introduces a new approach to domain adaptation in physics, addressing the fact that simulations often differ from experimental data not only in nuisances but also in the target quantity distribution. By studying a toy air‑shower benchmark with separate nuisance, simulation, and spectrum shifts, the authors show that standard adversarial adaptation can misalign spectra, leading to bias. They propose adaptive domain adaptation that reweights simulated events to focus on genuine physical mismatches and provide a label‑free rule for selecting the best model configuration.
By Ivan Kharuk (Institute for Nuclear Research of the Russian Academy of Sciences, Moscow Institute of Physics and Technology)
arXiv:2602. 00884v2 Announce Type: replace Abstract: Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics.
By Louis Serrano, Jiequn Han, Edouard Oyallon, Shirley Ho, Rudy Morel
The paper introduces a method for selecting the best neural‑operator model during deployment without needing high‑fidelity reference solutions. By using a squared Hilbert‑space loss, the authors show that ranking a finite library of models depends only on the low‑dimensional span of candidate differences, enabling simultaneous scoring of all models with a single anchor‑based linearized response of the governing equation. This shared physical diagnostic accurately recovered over 99.6% of pairwise preferences and 99.0% of optimal checkpoints across diverse Fourier and convolutional operator libraries for fluid, reaction‑diffusion, and wave dynamics, and often outperformed the best individual candidates.
By Hanbing Liang, Fujun Liu
arXiv:2601.12971v2 Announce Type: replace
Abstract: Physics-informed neural networks (PINNs) can be limited by coordinate representations and conflicting gradients from heterogeneous physical constra...
By Pancheng Niu, Jun Guo, Qiaolin He, Yongming Chen, Yanchao Shi