Title: Physics-Informed Graph Convolutional Network for Data-Free Learning of Channel Flow Fields
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: physics-informed machine learning, graph convolutional network, data-free, fluid dynamics, flow field prediction

Abstract: Physics-informed neural networks (PINNs) have gained traction for solving partial differential equations (PDEs) by embedding physical laws directly into the learning objective. However, traditional PINNs, typically built on fully connected neural networks, often struggle to capture localized interactions, scale poorly with mesh complexity, exhibit limited generalization across geometric variations and suffer from training instability due to minimal spatial representation. To address these challenges, we propose physics-informed graph convolutional network (PIGCN) architecture that leverages mesh connectivity to enforce local spatial coupling between variables, enhancing the ability of the model to learn structured physical relationships. In addition, this work investigated on data-free learning to reduce reliance on data observation and improve the generalization capability, introduced global physics loss, and implemented two-level dynamic weighting scheme to adaptively balance between multiple PDE residuals (e.g., continuity, momentum, energy) and composite loss terms (e.g., boundary conditions, global physics, and data), improving convergence in multi-objective training. We evaluated PIGCN against PINN on a square channel with isothermal walls and L-shaped channel with bending flow, which exhibits complex fluid dynamics phenomena. For square channel geometry, baseline PIGCN outperformed baseline PINN by 56.6\%, and was further improved with two-level dynamic weighting by 38.9\%, which achieved 66.6\% in rMSE error improvement compared to equivalent PINN. In L-shaped channel, baseline PIGCN improved rMSE error by 35.7\% against baseline PINN, and the introduction of global physics loss further reduced rMSE error by up to 71.3\% in comparison with baseline PIGCN. Our investigation also demonstrated that PIGCN achieved significantly faster training time and less graph memory consumption than PINN on various geometries, by 35.8\% and 62.7\% respectively. These results validated that graph architectures and hierarchical loss weighting can substantially enhance performance of physics-informed machine learning models for fluid dynamic analysis with scalable resource usage.