Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 29 of its 51 references that are in the map. First posted on arXiv 26 Jul 2026.
Builds on
29 of 51 references.
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17 more
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