Physics-Informed Coarsening for Multigrid Graph Neural Surrogates
This work proposes a multigrid graph neural network surrogate model for complex solid mechanics problems involving nonlinear elasticity, plasticity, and transient dynamics. The method employs an encoder-processor-decoder architecture and introduces a novel node-scoring mechanism based on physical residuals to drive adaptive coarsening on unstructured graphs, preferentially preserving regions of high strain or stress concentration in multiscale modeling. In contrast to conventional geometry-based downsampling heuristics, this strategy effectively maintains long-range interactions, significantly enhancing the stability and accuracy of long-time rollouts. Experimental results demonstrate that, across a range of linear and nonlinear transient scenarios, the proposed approach consistently outperforms standard sampling baselines in both predictive accuracy and rollout stability.