提出新型神经算子，高效模拟多区域耦合物理系统。
Physics-informed Partitioned Coupled Neural Operator for Complex Networks
- 在傅里叶层内设计联合卷积，统一建模多区域全局交互。
- 在气网测试中实现高精度仿真，模型复杂度低且泛化性强。
- 适合需跨区域耦合仿真的工程系统建模，如能源网络。
物理信息神经算子能高效、高保真地模拟由偏微分方程（PDEs）支配的系统。然而，现有研究大多仅关注单一空间区域内多尺度、多物理场系统，忽略了多个相互连接子区域的情况，如气体与热力系统的耦合。为此，本文提出物理信息分区耦合神经算子（PCNO），以提升此类网络的模拟性能。相较于现有的傅里叶神经算子（FNO），该方法在傅里叶层内设计了联合卷积算子，实现对所有子区域的全局信息融合；同时，在傅里叶层外引入网格对齐层，帮助联合卷积算子在频域中准确学习子区域间的耦合关系。在气网上的实验表明，所提算子不仅能精确模拟复杂系统，还具备良好的泛化能力与较低的模型复杂度。
原文摘要 · Abstract (English)
Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single spatial region, neglecting the case with multiple interconnected sub-regions, such as gas and thermal systems. To address this, this paper proposes a Physics-Informed Partitioned Coupled Neural Operator (PCNO) to enhance the simulation performance of such networks. Compared to the existing Fourier Neural Operator (FNO), this method designs a joint convolution operator within the Fourier layer, enabling global integration capturing all sub-regions. Additionally, grid alignment layers are introduced outside the Fourier layer to help the joint convolution operator accurately learn the coupling relationship between sub-regions in the frequency domain. Experiments on gas networks demonstrate that the proposed operator not only accurately simulates complex systems but also shows good generalization and low model complexity.
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