Learning Mesh-Based Simulation with Graph Networks

TL;DR

The paper tackles the high cost and inflexibility of traditional mesh-based simulations by introducing MeshGraphNets, a graph neural network framework that learns dynamics on adaptive meshes by performing mesh-space and world-space message passing. It combines an Encode-Process-Decode architecture with a learned sizing field to drive adaptive remeshing, enabling resolution-independent dynamics and efficient rollouts. Across cloth, structural, and fluid domains, the method delivers accurate predictions far faster than classical solvers and generalizes to larger or unseen meshes. This work broadens the applicability of neural simulators to complex, high-dimensional physical systems and opens avenues for differentiable optimization and control on adaptive meshes.

Abstract

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

Figures (8)

• Figure 1: Diagram of MeshGraphNets operating on our SphereDynamic domain (\vidspheredynamic). The model uses an Encode-Process-Decode architecture trained with one-step supervision, and can be applied iteratively to generate long trajectories at inference time. The encoder transforms the input mesh $M^t$ into a graph, adding extra world-space edges. The processor performs several rounds of message passing along mesh edges and world edges, updating all node and edge embeddings. The decoder extracts the acceleration for each node, which is used to update the mesh to produce $M^{t{+}1}$.
• Figure 2: Our model can predict dynamics of vastly different physical systems, from structural mechanics over cloth to fluid dynamics. We demonstrate this by simulating (a) a flag waving in the wind, (b) a deforming plate, (c) flow of water around a cylinder obstacle, and (d) the dynamics of air around the cross-section of an aircraft wing (\vidflagdynamic). The color map shows the von-Mises stress in (b), and the x-component of the velocity field in (c),(d).
• Figure 3: Simulation of a cloth interacting with a sphere. (a) In red, we highlight two nodes which are close in world-space but far in mesh-space, between which a world edge may be created. (b) With the same number of nodes, adaptive remeshing enables significantly more accurate simulations than a regular mesh with the same number of nodes.
• Figure 4: (a) Rollout of our model versus ground truth on dataset Airfoil. Adaptive meshing allows us to accurately predict dynamics at large and small scales. The grid-based U-Net baseline is capable of making good predictions at large scales, but it cannot resolve the smaller scales, despite using four times more cells than our model (\vidunetairfoil). (b) At inference time, our model can be scaled up to significantly larger and more complex setups than seen during training (\vidfunnel).
• Figure 5: (a) Our model outperforms GCN and CNN-based baselines. (b) GNS diverges on cloth datasets; providing mesh-space positions (GNS+mesh-pos) helps, but still fails on dynamic meshes. (c) Remeshing with learned or estimated sizing fields produces accurate rollouts. (d) Taking sufficient message passing steps is crucial for good performance, and limiting history size increases accuracy by preventing overfitting.