A novel residual multilayer perceptron-based graph convolutional network for modeling heat transfer and fluid flow

Conventional computational fluid dynamics methods are computationally intensive for tasks such as design optimization and real-time control, and while convolutional neural network-based surrogates potentially offer faster alternatives, their reliance on structured grids, static neighborhood definitions, and limited extrapolation capabilities highlights the need for more flexible and generalizable frameworks. Graph convolutional networks (GCNs), with their ability to operate on unstructured meshes and dynamically encode spatial relationships, offer a compelling alternative. In this work, a novel residual multilayer perceptron-based GCN (ResMLP-GCN) architecture is proposed, and its utility is demonstrated by applying it to three benchmark problems: (i) transient non-linear diffusion–advection problem, (ii) double lid-driven cavity flow, and (iii) backward-facing step flow. The developed models are trained on data from numerical simulations, using nodal coordinates and physical field variables as node features, employing a finite element-inspired hypergraph ϕ topology. The heat transfer model, trained on data from t=0 to 1000 s, accurately predicts the spatiotemporal evolution of temperature fields up to t=2000 s, maintaining relative errors below 8%. In the double lid-driven cavity problem, the model trained on Reynolds numbers ranging from 100 to 2000 achieves mean percentage errors under 14% when evaluated on extrapolated Reynolds numbers up to 3000. Similarly, for the backward-facing step, the model predicts the reattachment lengths for extrapolated Re with relative errors below 3%. These results highlight the potential of ResMLP-GCNs to capture complex spatiotemporal dynamics and generalize across temporal and parametric domains, offering a robust surrogate modeling strategy for heat and fluid flow problems.