Multiscale graph neural networks with adaptive mesh refinement for accelerating mesh-based simulations

TL;DR

This paper introduces a multiscale mesh-based GNN framework with adaptive mesh refinement, inspired by multigrid methods, to efficiently simulate complex multiphysics problems like phase field fracture, reducing training data needs and maintaining high accuracy.

Contribution

It develops a novel multiscale GNN approach with adaptive mesh refinement and transfer learning, improving efficiency and accuracy in mesh-based simulations of multiphysics problems.

Findings

Accelerated simulation times with high accuracy.

Effective use of transfer learning to reduce training data.

Mitigation of over-smoothing in fine mesh problems.

Abstract

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer from over-smoothing for problems involving very fine mesh. In this work, we develop a multiscale mesh-based GNN framework mimicking a conventional iterative multigrid solver, coupled with adaptive mesh refinement (AMR), to mitigate challenges with conventional mesh-based GNNs. We use the framework to accelerate phase field (PF) fracture problems involving coupled partial differential equations with a near-singular operator due to near-zero modulus inside the crack. We define the initial graph representation using all mesh resolution levels. We perform a series of downsampling steps using Transformer MP GNNs to reach the coarsest graph followed by upsampling steps to reach the original graph. We use skip connectors from the generated embedding during coarsening to prevent over-smoothing. We use Transfer Learning (TL) to significantly reduce the size of training datasets needed to simulate different crack configurations and loading conditions. The trained framework showed accelerated simulation times, while maintaining high accuracy for all cases compared to physics-based PF fracture model. Finally, this work provides a new approach to accelerate a variety of mesh-based engineering multiphysics problems