Multi-Hierarchical Surrogate Learning for Structural Dynamical Crash Simulations Using Graph Convolutional Neural Networks

TL;DR

The paper tackles the computational burden of high-fidelity crash simulations by introducing a multi-hierarchical surrogate framework that uses graph convolutional autoencoders (GCNNs) on mesh-simplified representations of a kart frame FE model. Surrogates are built sequentially from coarse to finer mesh resolutions, with transfer learning propagating global dynamics from coarse levels to residuals at finer levels, enabling accurate yet efficient time-dependent predictions. Key innovations include quadric-metric mesh downsampling/upsampling, Chebyshev-based graph convolutions, and a structured training regime MH1–MH3 that yields substantial speedups and improved accuracy over conventional POD/AE baselines. The results demonstrate that global crash dynamics are captured on coarse surrogates while microscale deformations are learned as refinements, with potential to support real-time multi-query evaluations and digital-twin applications in crashworthiness design.

Abstract

Crash simulations play an essential role in improving vehicle safety, design optimization, and injury risk estimation. Unfortunately, numerical solutions of such problems using state-of-the-art high-fidelity models require significant computational effort. Conventional data-driven surrogate modeling approaches create low-dimensional embeddings for evolving the dynamics in order to circumvent this computational effort. Most approaches directly operate on high-resolution data obtained from numerical discretization, which is both costly and complicated for mapping the flow of information over large spatial distances. Furthermore, working with a fixed resolution prevents the adaptation of surrogate models to environments with variable computing capacities, different visualization resolutions, and different accuracy requirements. We thus propose a multi-hierarchical framework for structurally creating a series of surrogate models for a kart frame, which is a good proxy for industrial-relevant crash simulations, at different levels of resolution. For multiscale phenomena, macroscale features are captured on a coarse surrogate, whereas microscale effects are resolved by finer ones. The learned behavior of the individual surrogates is passed from coarse to finer levels through transfer learning. In detail, we perform a mesh simplification on the kart model to obtain multi-resolution representations of it. We then train a graph-convolutional neural network-based surrogate that learns parameter-dependent low-dimensional latent dynamics on the coarsest representation. Subsequently, another, similarly structured surrogate is trained on the residual of the first surrogate using a finer resolution. This step can be repeated multiple times. By doing so, we construct multiple surrogates for the same system with varying hardware requirements and increasing accuracy.

Figures (12)

• Figure 1: Multi-hierarchical Surrogate modeling approach. Instead of learning on the full system discretization, we learn on a coarse representation of it. We then progressively refine the coarse representation by learning on the residual error. First, different levels of discretization are generated for the original model. On the coarsest level, a surrogate model is trained. If the error is not within the tolerance, the learned model is upsampled to the next level, and an additional surrogate is learned to capture the inaccuracies of the first one. The process is repeated until the error is within the tolerance or no more discretizations are left.
• Figure 2: Two example simulations of the the kart frame Shiiba2012 that serves as example of a structural mechanical crash system. From each simulation four snapshots at different points in time are used for the visualization.
• Figure 3: The first 50 normalized singular values of the training data as indicator of the Kolmogorov n-width.
• Figure 4: Differently resolved representations of the kart frame. The red dots represent the nodes.
• Figure 5: Graph convolutional autoencoder architecture with graph convolutional layers which operate on a mesh without pooling changing the number of features per node, fully-connected layers in the middle to reduce the dimensionality and an additional multilayer perceptron to capture the reduced dynamics.