# Differentiable Simulation of Soft Multi-body Systems

arXiv: https://arxiv.org/abs/2205.01758 · HTML: https://mlsanity.com/paper/2205.01758/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 79 references that are in the map.
- First posted on arXiv 3 May 2022.

## Builds on (most cited first, 29 of 29)

- [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)
- [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)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [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)
- [Robotic Pick-and-Place of Novel Objects in Clutter with Multi-Affordance Grasping and Cross-Domain Image Matching](https://mlsanity.com/paper/1710.01330/) (2017)
- [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)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [NeuralSim: Augmenting Differentiable Simulators with Neural Networks](https://mlsanity.com/paper/2011.04217/) (2020)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact](https://mlsanity.com/paper/2103.16021/) (2021)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [Codimensional Incremental Potential Contact](https://mlsanity.com/paper/2012.04457/) (2020)
- [Synthesis of Biologically Realistic Human Motion Using Joint Torque Actuation](https://mlsanity.com/paper/1904.13041/) (2019)
- [ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact](https://mlsanity.com/paper/2007.00987/) (2020)
- [Learning to Slide Unknown Objects with Differentiable Physics Simulations](https://mlsanity.com/paper/2005.05456/) (2020)
- [DiffAqua: A Differentiable Computational Design Pipeline for Soft Underwater Swimmers with Shape Interpolation](https://mlsanity.com/paper/2104.00837/) (2021)
- [Learning to Manipulate Amorphous Materials](https://mlsanity.com/paper/2103.02533/) (2021)
- [Soft Hybrid Aerial Vehicle via Bistable Mechanism](https://mlsanity.com/paper/2011.00426/) (2020)
- [Dynamic Grasping with a "Soft" Drone: From Theory to Practice](https://mlsanity.com/paper/2103.06465/) (2021)
- [Accurately Solving Physical Systems with Graph Learning](https://mlsanity.com/paper/2006.03897/) (2020)

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

- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [PhysTwin: Physics-Informed Reconstruction and Simulation of Deformable Objects from Videos](https://mlsanity.com/paper/2503.17973/) (2025)
- [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)
- [GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulation](https://mlsanity.com/paper/2406.14927/) (2024)
- [Dynamic 3D Gaussian Tracking for Graph-Based Neural Dynamics Modeling](https://mlsanity.com/paper/2410.18912/) (2024)
- [DiffuseBot: Breeding Soft Robots With Physics-Augmented Generative Diffusion Models](https://mlsanity.com/paper/2311.17053/) (2023)
- [RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimation](https://mlsanity.com/paper/2205.05678/) (2022)
- [DexDeform: Dexterous Deformable Object Manipulation with Human Demonstrations and Differentiable Physics](https://mlsanity.com/paper/2304.03223/) (2023)
- [ClothesNet: An Information-Rich 3D Garment Model Repository with Simulated Clothes Environment](https://mlsanity.com/paper/2308.09987/) (2023)
- [SAM-RL: Sensing-Aware Model-Based Reinforcement Learning via Differentiable Physics-Based Simulation and Rendering](https://mlsanity.com/paper/2210.15185/) (2022)
- [Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulation](https://mlsanity.com/paper/2412.12089/) (2024)
- [Vid2Sim: Generalizable, Video-based Reconstruction of Appearance, Geometry and Physics for Mesh-free Simulation](https://mlsanity.com/paper/2506.06440/) (2025)
- [DiffMimic: Efficient Motion Mimicking with Differentiable Physics](https://mlsanity.com/paper/2304.03274/) (2023)
- [Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization](https://mlsanity.com/paper/2406.04155/) (2024)
- [UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation](https://mlsanity.com/paper/2505.16971/) (2025)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [NeuralFluid: Neural Fluidic System Design and Control with Differentiable Simulation](https://mlsanity.com/paper/2405.14903/) (2024)
- [MASIV: Toward Material-Agnostic System Identification from Videos](https://mlsanity.com/paper/2508.01112/) (2025)
- [Differentiable Hybrid Traffic Simulation](https://mlsanity.com/paper/2210.08046/) (2022)
- [Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?](https://mlsanity.com/paper/2207.05060/) (2022)
- [Differentiable Visual Computing for Inverse Problems and Machine Learning](https://mlsanity.com/paper/2312.04574/) (2023)
- [Real2Sim2Real Transfer for Control of Cable-driven Robots via a Differentiable Physics Engine](https://mlsanity.com/paper/2209.06261/) (2022)
- [DiffVL: Scaling Up Soft Body Manipulation using Vision-Language Driven Differentiable Physics](https://mlsanity.com/paper/2312.06408/) (2023)
- [One-Shot Real-to-Sim via End-to-End Differentiable Simulation and Rendering](https://mlsanity.com/paper/2412.00259/) (2024)
- [MOSIV: Multi-Object System Identification from Videos](https://mlsanity.com/paper/2603.06022/) (2026)
- [Learning Object Manipulation Skills from Video via Approximate Differentiable Physics](https://mlsanity.com/paper/2208.01960/) (2022)
- [Implicit Neural Representation for Physics-driven Actuated Soft Bodies](https://mlsanity.com/paper/2401.14861/) (2024)
- [Learning Object Properties Using Robot Proprioception via Differentiable Robot-Object Interaction](https://mlsanity.com/paper/2410.03920/) (2024)
- [Hierarchical Multi-Agent Reinforcement Learning with Control Barrier Functions for Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2507.14850/) (2025)

## Abstract (arXiv)

We present a method for differentiable simulation of soft articulated bodies. Our work enables the integration of differentiable physical dynamics into gradient-based pipelines. We develop a top-down matrix assembly algorithm within Projective Dynamics and derive a generalized dry friction model for soft continuum using a new matrix splitting strategy. We derive a differentiable control framework for soft articulated bodies driven by muscles, joint torques, or pneumatic tubes. The experiments demonstrate that our designs make soft body simulation more stable and realistic compared to other frameworks. Our method accelerates the solution of system identification problems by more than an order of magnitude, and enables efficient gradient-based learning of motion control with soft robots.