# Rigid-Deformation Decomposition AI Framework for 3D Spatio-Temporal Prediction of Vehicle Collision Dynamics

arXiv: https://arxiv.org/abs/2503.19712 · HTML: https://mlsanity.com/paper/2503.19712/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 53 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Builds on (most cited first, 16 of 16)

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- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Efficient Large-Scale Traffic Forecasting with Transformers: A Spatial Data Management Perspective](https://mlsanity.com/paper/2412.09972/) (2024)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulations](https://mlsanity.com/paper/2402.13101/) (2024)
- [Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsampling](https://mlsanity.com/paper/2503.17941/) (2025)
- [Model-Agnostic AI Framework with Explicit Time Integration for Long-Term Fluid Dynamics Prediction](https://mlsanity.com/paper/2412.05657/) (2024)

## Built on by (most cited first, 1 of 1)

- [Point-wise Diffusion Models for Physical Systems with Shape Variations: Application to Spatio-temporal and Large-scale system](https://mlsanity.com/paper/2508.01230/) (2025)

## Abstract (arXiv)

This study presents a rigid-deformation decomposition framework for vehicle collision dynamics that mitigates the spectral bias of implicit neural representations, that is, coordinate-based neural networks that directly map spatio-temporal coordinates to physical fields. We introduce a hierarchical architecture that decouples global rigid-body motion from local deformation using two scale-specific networks, denoted as RigidNet and DeformationNet. To enforce kinematic separation between the two components, we adopt a frozen-anchor training strategy combined with a quaternion-incremental scheme. This strategy alleviates the kinematic instability observed in joint training and yields a 29.8% reduction in rigid-body motion error compared with conventional direct prediction schemes. The stable rigid-body anchor improves the resolution of high-frequency structural buckling, which leads to a 17.2% reduction in the total interpolation error. Loss landscape analysis indicates that the decomposition smooths the optimization surface, which enhances robustness to distribution shifts in angular extrapolation and yields a 46.6% reduction in error. To assess physical validity beyond numerical accuracy, we benchmark the decomposed components against an oracle model that represents an upper bound on performance. The proposed framework recovers 92% of the directional correlation between rigid and deformation components and 96% of the spatial deformation localization accuracy relative to the oracle, while tracking the temporal energy dynamics with an 8 ms delay. These results demonstrate that rigid-deformation decomposition enables accurate and physically interpretable predictions for nonlinear collision dynamics.