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.
Model Comparison
Comparison of mesh-based physical simulation models. Dynamic hierarchy refers to hierarchical graph structures that evolve over time. Adaptive indicates that the graph structures are determined by physical inputs. Prop. denotes feature propagation.
Model Architecture
Physical dynamics is modeled on multiple graph resolutions with adaptive structures, \(\mathcal{G}_1, \mathcal{G}_2, \ldots, \mathcal{G}_L\), and are processed using their respective AMP layers. The \(\texttt{DiffSELECT}\) operation performs differentiable pooling to create coarser graphs with learnable downsampling probabilities. \(\texttt{REDUCE}\) and \(\texttt{EXPAND}\) integrate inter-level information using learned feature aggregation weights over the neighboring nodes. EvoMesh is trained end-to-end with one-step supervision.
