Quantum SEDONet is a quantum-enhanced deep operator network that embeds spectral features—Fourier for periodic coordinates and Chebyshev for bounded, non‑periodic coordinates—directly into the trunk network. This coordinate‑wise spectral embedding is achieved without adding qubits or circuit depth under unary amplitude encoding, and it reduces mean relative L2 error by up to 54.1% across four PDE benchmarks compared to the baseline Quantum DeepONet. The method demonstrates that quantum and classical inference paths agree to within 10⁻⁸, and it allows simultaneous use of both spectral bases within a single problem, as shown in a mixed‑boundary Poisson channel example.
By Muhammad Abid, Arth Sojitra, Bipin Tiwari, Omer San
arXiv:2603. 13751v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs).
By Zhangyong Liang, Huanhuan Gao
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
By Haoze Song, Zhihao Li, Xiaobo Zhang, Zecheng Gan, Zhilu Lai, Wei Wang
arXiv:2609.35938v1 Announce Type: new
Abstract: This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitl...
By Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu
arXiv:2609. 23529v1 Announce Type: new Abstract: Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment.
By Hang-Cheng Dong, Pengcheng Cheng
arXiv:2606. 28122v1 Announce Type: cross Abstract: Neural operators provide deep neural networks for learning mappings between function spaces.
By Alex Colagrande, Paul Caillon, Eva Feillet, Alexandre Allauzen
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
Helix‑FNO is a teacher‑student framework that couples a 32‑state mechanistic model with a Fourier neural operator to learn the full solution operator for full‑scale treatment processes. The teacher generates a high‑fidelity dataset via Latin‑hypercube sampling and active learning, while the student learns in the spectral domain, enabling generalisation across varying influent profiles, controls, and plant layouts. The resulting operator achieves millisecond inference, three orders of magnitude faster than the mechanistic teacher, and is evaluated against physics‑informed and data‑driven surrogates on accuracy, dataset efficiency, and latency, positioning it on a speed‑accuracy Pareto front.
By Jiabao Zhao, Chuwei Wang, Jinxi Yang
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. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
By Kelan Gray, Finlay Brown, Nicolas Boull\'e, Matthew J. Colbrook
Transolver‑σ is a neural PDE solver that jointly models spectral and physical subspaces to improve accuracy in both one‑step and autoregressive rollouts. The method uses adaptive physical-state interactions, Slice‑Residual Physics‑Attention, and an axis‑factorized Fourier operator to enable information exchange between representations. Across five standard PDE benchmarks, Transolver‑σ reduces benchmark‑averaged relative error by 33.4% compared to the strongest baseline and shows strong performance on coupled multiphysics systems and real‑world fluid and combustion data.
By Haonan Shangguan, Hang Zhou, Haixu Wu, Yuezhou Ma, Jianmin Wang, Mingsheng Long
arXiv:2607. 12570v1 Announce Type: cross Abstract: Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations.
By Marc Haltmayer, Jaemin Seo, Yuseung Lee, Sungyeop Lee, Jaehoon Jeong, Jae Yong Lee