EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions

TL;DR

EvoMesh is a novel, fully differentiable framework that adaptively learns hierarchical graph structures and physical dynamics for mesh-based simulations, significantly improving performance on benchmark datasets.

Contribution

It introduces a differentiable method to jointly learn graph hierarchies and physical dynamics, enabling adaptive and more accurate physical simulations.

Findings

Outperforms recent fixed-hierarchy message passing networks on benchmarks.

Effectively captures long-range dependencies in physical systems.

Demonstrates flexibility and improved accuracy in large-scale simulations.

Abstract

Graph neural networks have been a powerful tool for mesh-based physical simulation. To efficiently model large-scale systems, existing methods mainly employ hierarchical graph structures to capture multi-scale node relations. However, these graph hierarchies are typically manually designed and fixed, limiting their ability to adapt to the evolving dynamics of complex physical systems. We propose EvoMesh, a fully differentiable framework that jointly learns graph hierarchies and physical dynamics, adaptively guided by physical inputs. EvoMesh introduces anisotropic message passing, which enables direction-specific aggregation of dynamic features between nodes within each hierarchy, while simultaneously learning node selection probabilities for the next hierarchical level based on physical context. This design creates more flexible message shortcuts and enhances the model's capacity to capture long-range dependencies. Extensive experiments on five benchmark physical simulation datasets show that EvoMesh outperforms recent fixed-hierarchy message passing networks by large margins. The project page is available at https://hbell99.github.io/evo-mesh/.