Physics-informed Partitioned Coupled Neural Operator for Complex Networks

TL;DR

This paper introduces a Physics-Informed Partitioned Coupled Neural Operator (PCNO) that improves simulation accuracy and efficiency for interconnected multi-region systems governed by PDEs, such as gas and thermal networks.

Contribution

The paper proposes a novel PCNO that integrates joint convolution and grid alignment layers to effectively model coupled multi-region systems, extending neural operators to more complex interconnected domains.

Findings

Accurately simulates complex interconnected systems

Demonstrates good generalization to unseen data

Maintains low model complexity

Abstract

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.