Physics-informed Partitioned Coupled Neural Operator for Complex Networks
This work addresses a domain-specific problem for simulating complex multi-region networks in physics and engineering, representing an incremental improvement over existing methods.
The paper tackles the simulation of interconnected sub-region systems like gas and thermal networks, which existing physics-informed neural operators neglect, and proposes a Physics-Informed Partitioned Coupled Neural Operator (PCNO) that demonstrates accurate simulation, good generalization, and low model complexity in experiments on gas networks.
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.