# Efficient Differentiable Simulation of Articulated Bodies

arXiv: https://arxiv.org/abs/2109.07719 · HTML: https://mlsanity.com/paper/2109.07719/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 77 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 30 of 41)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics](https://mlsanity.com/paper/2104.03311/) (2021)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [NeuralSim: Augmenting Differentiable Simulators with Neural Networks](https://mlsanity.com/paper/2011.04217/) (2020)
- [Memory-Efficient Backpropagation Through Time](https://mlsanity.com/paper/1606.03401/) (2016)
- [Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE](https://mlsanity.com/paper/2006.02493/) (2020)

## Built on by (most cited first, 30 of 39)

- [Accelerated Policy Learning with Parallel Differentiable Simulation](https://mlsanity.com/paper/2204.07137/) (2022)
- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [NeuPhysics: Editable Neural Geometry and Physics from Monocular Videos](https://mlsanity.com/paper/2210.12352/) (2022)
- [DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Tools](https://mlsanity.com/paper/2203.17275/) (2022)
- [Differentiable Simulation of Soft Multi-body Systems](https://mlsanity.com/paper/2205.01758/) (2022)
- [Differentiable Dynamics for Articulated 3d Human Motion Reconstruction](https://mlsanity.com/paper/2205.12256/) (2022)
- [RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimation](https://mlsanity.com/paper/2205.05678/) (2022)
- [Rethinking Optimization with Differentiable Simulation from a Global Perspective](https://mlsanity.com/paper/2207.00167/) (2022)
- [Atlas3D: Physically Constrained Self-Supporting Text-to-3D for Simulation and Fabrication](https://mlsanity.com/paper/2405.18515/) (2024)
- [Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulation](https://mlsanity.com/paper/2412.12089/) (2024)
- [Dress-1-to-3: Single Image to Simulation-Ready 3D Outfit with Diffusion Prior and Differentiable Physics](https://mlsanity.com/paper/2502.03449/) (2025)
- [Guided Data Augmentation for Offline Reinforcement Learning and Imitation Learning](https://mlsanity.com/paper/2310.18247/) (2023)
- [NeuralFluid: Neural Fluidic System Design and Control with Differentiable Simulation](https://mlsanity.com/paper/2405.14903/) (2024)
- [Differentiable Hybrid Traffic Simulation](https://mlsanity.com/paper/2210.08046/) (2022)
- [Gradient Informed Proximal Policy Optimization](https://mlsanity.com/paper/2312.08710/) (2023)
- [Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?](https://mlsanity.com/paper/2207.05060/) (2022)
- [Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contact](https://mlsanity.com/paper/2309.04710/) (2023)
- [Understanding when Dynamics-Invariant Data Augmentations Benefit Model-Free Reinforcement Learning Updates](https://mlsanity.com/paper/2310.17786/) (2023)
- [Neural Field Dynamics Model for Granular Object Piles Manipulation](https://mlsanity.com/paper/2311.00802/) (2023)
- [Learning Object Manipulation Skills from Video via Approximate Differentiable Physics](https://mlsanity.com/paper/2208.01960/) (2022)
- [Improving Gradient Computation for Differentiable Physics Simulation with Contacts](https://mlsanity.com/paper/2305.00092/) (2023)
- [Accelerating Visual-Policy Learning through Parallel Differentiable Simulation](https://mlsanity.com/paper/2505.10646/) (2025)
- [Leveraging Reward Gradients For Reinforcement Learning in Differentiable Physics Simulations](https://mlsanity.com/paper/2203.02857/) (2022)
- [Traffic-Aware Autonomous Driving with Differentiable Traffic Simulation](https://mlsanity.com/paper/2210.03772/) (2022)
- [Differentiable Analog Quantum Computing for Optimization and Control](https://mlsanity.com/paper/2210.15812/) (2022)
- [Stabilizing Backpropagation Through Time to Learn Complex Physics](https://mlsanity.com/paper/2405.02041/) (2024)
- [Gradient-based Trajectory Optimization with Parallelized Differentiable Traffic Simulation](https://mlsanity.com/paper/2412.16750/) (2024)
- [Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisions](https://mlsanity.com/paper/2503.11269/) (2025)
- [Diff-Transfer: Model-based Robotic Manipulation Skill Transfer via Differentiable Physics Simulation](https://mlsanity.com/paper/2310.04930/) (2023)
- [Accelerated Learning with Linear Temporal Logic using Differentiable Simulation](https://mlsanity.com/paper/2506.01167/) (2025)

## Abstract (arXiv)

We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on articulated bodies. We derive the gradients of the forward dynamics using spatial algebra and the adjoint method. Our approach is an order of magnitude faster than autodiff tools. By only saving the initial states throughout the simulation process, our method reduces memory requirements by two orders of magnitude. We demonstrate the utility of efficient differentiable dynamics for articulated bodies in a variety of applications. We show that reinforcement learning with articulated systems can be accelerated using gradients provided by our method. In applications to control and inverse problems, gradient-based optimization enabled by our work accelerates convergence by more than an order of magnitude.