Physics-informed partitioned coupled neural operator for complex networks

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations. 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 network systems. To address this, this paper proposes a Physics-Informed Partitioned Coupled Neural Operator to enhance the simulation performance of such networks. Compared to the existing Fourier Neural Operator, this method designs a joint convolution operator within the Fourier layers, enabling global integration capturing all sub-regions. Additionally, grid alignment layers are introduced outside the Fourier layers to help the joint convolution operator accurately learn the coupling relationship between sub-regions in the frequency domain. Experiments on gas, petroleum and transportation networks demonstrate that the proposed operator not only accurately simulates these complex networks but also shows good generalization and low model complexity.