Physics-Informed Coarsening for Multigrid Graph Neural Surrogates

2026-05-29

AI Summary

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.

Abstract

Learning-based surrogates for partial differential equations have recently matched the accuracy of classical solvers while achieving orders-of-magnitude speedups, predominantly in fluid settings and structured geometries. In contrast, robust surrogates for deformable solids remain underexplored, despite the presence of nonlinear elasticity, plasticity, and transient behavior that challenge standard architectures. We introduce a multigrid graph neural network for solid mechanics that couples an encoder-processor-decoder backbone with a physics-informed coarsening strategy. Instead of downsampling via geometric heuristics, our method scores nodes using a residual-based measure of local physical activity and preferentially retains regions of high strain or stress concentration, allocating multiscale capacity where it is most needed. This preserves long-range interactions through hierarchical message passing while improving stability over long rollouts. We evaluate on multiple datasets covering linear, nonlinear, and transient regimes, and observe consistent gains in accuracy and rollout stability compared to standard sampling baselines. Our results highlight the importance of physics-informed coarsening for scalable surrogate modeling in solid mechanics.

Problem

• solid mechanics
• nonlinear elasticity
• plasticity
• transient behavior
• surrogate modeling

Innovation

• physics-informed coarsening
• multigrid graph neural network
• solid mechanics
• residual-based scoring
• hierarchical message passing