Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamics

TL;DR

GNSS addresses the challenge of time-resolved structural dynamics by learning a graph-based surrogate that advances the solution with a fixed physical timestep. It uses node-fixed local coordinates, a sign-aware acceleration loss, and a wavelength-informed connectivity to capture wave dynamics efficiently. In a guided-wave beam case, GNSS achieves accurate long-horizon rollouts and generalizes to unseen loading, while delivering substantial speedups over explicit FEM solvers. The results suggest locality-preserving graph networks with physics-informed updates as a competitive direction for dynamic structural simulations and motivate extension to 3D elastodynamics and experimental data.

Abstract

Graph Neural Networks (GNNs) have recently been explored as surrogate models for numerical simulations. While their applications in computational fluid dynamics have been investigated, little attention has been given to structural problems, especially for dynamic cases. To address this gap, we introduce the Graph Network-based Structural Simulator (GNSS), a GNN framework for surrogate modeling of dynamic structural problems. GNSS follows the encode-process-decode paradigm typical of GNN-based machine learning models, and its design makes it particularly suited for dynamic simulations thanks to three key features: (i) expressing node kinematics in node-fixed local frames, which avoids catastrophic cancellation in finite-difference velocities; (ii) employing a sign-aware regression loss, which reduces phase errors in long rollouts; and (iii) using a wavelength-informed connectivity radius, which optimizes graph construction. We evaluate GNSS on a case study involving a beam excited by a 50kHz Hanning-modulated pulse. The results show that GNSS accurately reproduces the physics of the problem over hundreds of timesteps and generalizes to unseen loading conditions, where existing GNNs fail to converge or deliver meaningful predictions. Compared with explicit finite element baselines, GNSS achieves substantial inference speedups while preserving spatial and temporal fidelity. These findings demonstrate that locality-preserving GNNs with physics-consistent update rules are a competitive alternative for dynamic, wave-dominated structural simulations.

Figures (14)

• Figure 1: Visual representation of information propagation over two message-passing steps. In the second step, colored nodes receive messages from the same neighbors as in the first step, since the topology is fixed. However, these neighbors now carry the information acquired from their own neighbors in the previous step, illustrated using a grayscale colormap.
• Figure 2: Our GNSS framework, adapted from sanchez2020learning's work. a) Rollout: an initial configuration $X_0$ is provided, then the GNSS is iteratively applied $T$ times to predict the trajectory from time 0 to time T. GNSS includes a graph building procedure, a GNN, and a fixed updater. b) Encode-process-decode procedure. c) Message passing operation at message passing step $m$ with $m=1,\dots, M$.
• Figure 3: Graph defined through connectivity radius.
• Figure 4: Representation of the encoder block: two MLPs, $\epsilon^v_{\Theta^v}$ and $\epsilon^e_{\Theta^e}$, embed the node and edge feature vectors, respectively, into the latent space.
• Figure 5: Message construction: an MLP merges the information from each link (2 nodes and 1 edge) into an update edge feature.