Model Releases
Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs
arXiv:2607.23466v1 Announce Type: new Abstract: Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator method
arXiv:2607.23466v1 Announce Type: new Abstract: Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited. We extend Fourier neural operators (FNOs) with minimal architectural modifications along two directions. For parameterized dynamics, we propose a hypernetwork-based modulation that conditions the operator on physical parameters. For coupled systems, we conduct a systematic exploration of architectural choices, examining how operator components can be adapted to balance shared structure with cross-variable interactions while retaining the efficiency of standard FNOs. Evaluations on benchmark PDEs, including the one-dimensional capacitively coupled plasma equations and the Gray-Scott system, show that our methods achieve up to 55-72% lower errors than strong baselines, demonstrating the effectiveness of principled modulation and systematic design exploration.
Related
- HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
- Shearlet Neural Operators for Anisotropic-Shock-Dominated and Multi-scale parametric partial differential equations
- Imposing Boundary Conditions on Neural Operators via Learned Function Extensions
- WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations
Source: arXiv cs.LG | 2026-07-28