发表机构
Arizona State University; Applied Materials Inc.（亚利桑那州立大学; 应用材料公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对参数化和耦合偏微分方程建模问题，通过最少架构修改扩展傅里叶神经算子。对参数化动力学用超网络调制，对耦合系统探索架构选择，实验表明该方法比基线误差大幅降低，有效提升了偏微分方程建模效果。
AI 中文摘要
参数化和耦合偏微分方程在科学与工程现象建模中至关重要，但能同时处理这两方面的神经算子方法仍有限。我们沿两个方向对傅里叶神经算子（FNOs）进行最少架构修改来扩展。对于参数化动力学，提出基于超网络的调制，根据物理参数调整算子。对于耦合系统，系统探索架构选择，研究算子组件如何在保持标准FNOs效率的同时，平衡共享结构与交叉变量交互。在包括一维电容耦合等离子体方程和Gray - Scott系统等基准偏微分方程上的评估表明，我们的方法比强大基线误差低55 - 72%，证明了有原则调制和系统设计探索的有效性。
英文摘要
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.
CommentsAccepted to ICLR 2026
