Rigid-Deformation Decomposition
AI Framework for 3D Vehicle Collision Dynamics

Sanghyuk Kima, Minsik Seob, Sunwoong Yangc,d,*, Namwoo Kangb,c,**
aDept. of Mechanical Engineering, KAIST   bNarnia Labs   cCho Chun Shik Graduate School of Mobility, KAIST   dDept. of Mechanical Engineering, Hanyang University
Advanced Engineering Informatics (2026)
Try Live Demo Paper How It Works Results

A hierarchical deep learning framework that decouples global rigid-body motion from local structural deformation, enabling real-time 3D spatio-temporal prediction of full-scale vehicle crash dynamics.

Interactive Demo

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Key Contributions

1

Multi-scale decomposition overcomes spectral bias

RigidNet captures low-frequency global motion; DeformationNet resolves high-frequency structural buckling — addressing the spectral bias that causes single-network architectures to smooth over critical failure modes.

2

Frozen-anchor training ensures kinematic stability

A sequential training strategy freezes RigidNet as a kinematic anchor, yielding 17.2% lower total error than the best unified baseline and 29.8% lower rigid-body error than joint training.

3

Physically consistent and validated against oracle

Recovers 92% directional correlation and 96% deformation localization accuracy vs. oracle, with 1.8% peak frontal intrusion error.

Why Decompose?

Collision behavior consists of two coupled components: rigid-body motion, which governs post-crash vehicle trajectory and secondary accident risk, and structural deformation, which captures crush, intrusion, and occupant safety-related damage. Standard single networks cannot separate these entangled scales.

G

Global rigid-body motion

Low-frequency translation and rotation driven by inertia. Smooth trajectory over the full 0.4 s collision.

L

Local structural deformation

High-frequency buckling and plastic hinging in the frontal region. Transient peaks within milliseconds of impact.

Standard neural networks exhibit spectral bias toward low-frequency components, plateauing at ~2.0×10-3 MSE regardless of architecture. Our decomposition breaks through this ceiling.

Proposed Framework

Framework overview
RigidNet (3-layer MLP) predicts global rigid-body motion. DeformationNet (6-layer MLP) predicts residual deformation. Stage 1 trains RigidNet; Stage 2 freezes it as a kinematic anchor and trains DeformationNet. Total: ~404K parameters, ~20 min training, 8 ms inference. Collision scenarios are parameterized by velocity (40–80 km/h), angle (0–45°), offset ratio (5–100%), and standoff distance (0.1–2.0 m).

Results

Baseline Comparison (~400K params each)

ModelArchitectureVal MSE (×10-3)
DeepONetUnified (Operator)3.22
Coupled MLPUnified (MLP)2.04
TransolverUnified (Transformer)1.92 ± 0.07
Proposed (Ours)Decomposed1.69 ± 0.02

Optimization Landscape

Decomposition transforms the loss surface from sharp, isolated minima into a broad flat basin.

2D loss landscape comparison
The unified model converges to a sharp minimum with large train-validation gap. The proposed decomposition forms a flat basin matching the oracle's landscape.
1D loss interpolation
1D loss interpolation between independently trained solutions. The unified model (a) shows high-loss barriers between minima; the proposed (b) and oracle (c) models form smooth, connected basins.