# A Deep Emulator for Secondary Motion of 3D Characters

arXiv: https://arxiv.org/abs/2103.01261 · HTML: https://mlsanity.com/paper/2103.01261/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [SoftSMPL: Data-driven Modeling of Nonlinear Soft-tissue Dynamics for Parametric Humans](https://mlsanity.com/paper/2004.00326/) (2020)
- [Realtime Simulation of Thin-Shell Deformable Materials using CNN-Based Mesh Embedding](https://mlsanity.com/paper/1909.12354/) (2019)
- [Complementary Dynamics](https://mlsanity.com/paper/2009.02462/) (2020)
- [Alternating ConvLSTM: Learning Force Propagation with Alternate State Updates](https://mlsanity.com/paper/2006.07818/) (2020)

## Built on by (most cited first, 16 of 16)

- [TextDeformer: Geometry Manipulation using Text Guidance](https://mlsanity.com/paper/2304.13348/) (2023)
- [Thermodynamics-informed graph neural networks](https://mlsanity.com/paper/2203.01874/) (2022)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [HeadEvolver: Text to Head Avatars via Expressive and Attribute-Preserving Mesh Deformation](https://mlsanity.com/paper/2403.09326/) (2024)
- [Temporal Residual Jacobians For Rig-free Motion Transfer](https://mlsanity.com/paper/2407.14958/) (2024)
- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [Active Learning of Neural Collision Handler for Complex 3D Mesh Deformations](https://mlsanity.com/paper/2110.07727/) (2021)
- [Towards High-Quality 3D Motion Transfer with Realistic Apparel Animation](https://mlsanity.com/paper/2407.11266/) (2024)
- [AutoAvatar: Autoregressive Neural Fields for Dynamic Avatar Modeling](https://mlsanity.com/paper/2203.13817/) (2022)
- [Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks](https://mlsanity.com/paper/2201.10122/) (2022)
- [A Neural-Network-Based Approach for Loose-Fitting Clothing](https://mlsanity.com/paper/2404.16896/) (2024)
- [Attention is All They Need: Exploring the Media Archaeology of the Computer Vision Research Paper](https://mlsanity.com/paper/2209.11200/) (2022)
- [Momentum-Conserving Graph Neural Networks for Deformable Objects](https://mlsanity.com/paper/2604.26097/) (2026)
- [Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes](https://mlsanity.com/paper/2607.24954/) (2026)

## Abstract (arXiv)

Fast and light-weight methods for animating 3D characters are desirable in various applications such as computer games. We present a learning-based approach to enhance skinning-based animations of 3D characters with vivid secondary motion effects. We design a neural network that encodes each local patch of a character simulation mesh where the edges implicitly encode the internal forces between the neighboring vertices. The network emulates the ordinary differential equations of the character dynamics, predicting new vertex positions from the current accelerations, velocities and positions. Being a local method, our network is independent of the mesh topology and generalizes to arbitrarily shaped 3D character meshes at test time. We further represent per-vertex constraints and material properties such as stiffness, enabling us to easily adjust the dynamics in different parts of the mesh. We evaluate our method on various character meshes and complex motion sequences. Our method can be over 30 times more efficient than ground-truth physically based simulation, and outperforms alternative solutions that provide fast approximations.