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March 26, 2026Open Access

Improvement of the accuracy of surrogate models for thermal stress analysis using multiple graph neural networks

Key Points

The research aims to improve the accuracy of surrogate models for thermal stress analysis using graph neural networks.
Developed multiple GNN architectures for CAE simulations.
Evaluated three graph structures for node selection.
Conducted finite element method simulations to generate stress distributions.
Applied five-fold cross-validation to assess improvements in model accuracy.
Achieved R² improvement from 0.80/0.76 to 0.88/0.80 with coarse lattice method.
Long-range edges further increased ST prediction accuracy to 0.82.
Demonstrated capability for deeper networks without overfitting.

Abstract

This study proposes graph neural network (GNN) architectures to accelerate Computer Aided Engineering (CAE) simulations by building fast surrogate models. Three graph structures were evaluated: (i) purely random node selection, (ii) a coarse lattice in the xy-plane combined with random nodes, and (iii) the same structure as (ii) plus long-range edges in the z-direction. Finite element method simulations generated stress distributions (axial SZ and circumferential ST) from various temperature fields in a cylindrical model consisting of ~10,000 triangular mesh nodes. Five-fold cross-validation showed that (ii) improved R² from 0.80/0.76 to 0.88/0.80 compared to (i), and (iii) further increased ST prediction to 0.82. The proposed architectures also allowed deeper networks with more hidden units without overfitting. These results demonstrate that coarse lattices and long-range edges effectively enhance both accuracy and generalization for ML-based CAE surrogate modeling

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