Modeling subgrid scale production rates on complex meshes using graph neural networks

Abstract

Large-eddy simulations (LES) require closures for filtered production rates because the resolved fields do not contain all correlations that govern chemical source terms. We develop a graph neural network (GNN) that predicts filtered species production rates on non-uniform meshes from inputs of filtered mass fractions and temperature. Direct numerical simulations of turbulent premixed hydrogen-methane jet flames with hydrogen fractions of 10%, 50%, and 80% provide the dataset. All fields are Favre filtered with the filter width matched to the operating mesh, and learning is performed on subdomain graphs constructed from mesh-point connectivity. A compact set of reactants, intermediates, and products is used, and their filtered production rates form the targets. The model is trained on 10% and 80% blends and evaluated on the unseen 50% blend to test cross-composition generalization. The GNN is compared against an unclosed reference that evaluates rates at the filtered state, and a convolutional neural network baseline that requires remeshing. Across in-distribution and out-of-distribution cases, the GNN yields lower errors and closer statistical agreement with the reference data. Furthermore, the model demonstrates robust generalization across varying filter widths without retraining, maintaining bounded errors at coarser spatial resolutions. A backward facing step configuration further confirms prediction efficacy on a practically relevant geometry. These results highlight the capability of GNNs as robust data-driven closure models for LES on complex meshes.

Figures (6)

• Figure 1: A schematic of the GNN framework for modeling subgrid-scale production rates.
• Figure 2: Contours of GNN predictions for in-distribution test cases. Columns 1 and 2 display the H10 case, showing species production rates (in $\mathrm{kg \ m^{-3} \ s^{-1}}$) at the domain midplane and corresponding percentage errors relative to filtered DNS data, respectively. Columns 3 and 4 present the same quantities for the H80 test case.
• Figure 3: Contours demonstrating superiority of GNN compared to other approaches for H50. Column 1: Contours of production rates of key species (in $\mathrm{kg\,m^{-3}\,s^{-1}}$) shown for the domain midplane. Columns 2, 3, 4: Contours of percentage errors between ground truth (filtered from DNS solution) and the results of no-model, CNN, and GNN.
• Figure 4: Joint PDFs computed between production rates obtained from no-model/CNN/GNN and ground truth. Magenta line represents the $y=x$ reference curve, within the extents of GNN prediction. $R^2$ score mentioned in subplot title (no-model/CNN/GNN).
• Figure 5: Contours demonstrating the prediction error incurred by the GNN for the unseen H50 flame across varying filter widths. Percentage errors for the 12$\times$ downsampling factor are presented in Column 1 and for the 16$\times$ downsampling factor in Column 2.