# SoftMAC: Differentiable Soft Body Simulation with Forecast-based Contact Model and Two-way Coupling with Articulated Rigid Bodies and Clothes

arXiv: https://arxiv.org/abs/2312.03297 · HTML: https://mlsanity.com/paper/2312.03297/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [ManiSkill2: A Unified Benchmark for Generalizable Manipulation Skills](https://mlsanity.com/paper/2302.04659/) (2023)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [SoftGym: Benchmarking Deep Reinforcement Learning for Deformable Object Manipulation](https://mlsanity.com/paper/2011.07215/) (2020)
- [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)
- [The ThreeDWorld Transport Challenge: A Visually Guided Task-and-Motion Planning Benchmark for Physically Realistic Embodied AI](https://mlsanity.com/paper/2103.14025/) (2021)
- [DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact](https://mlsanity.com/paper/2106.05306/) (2021)
- [Theano: A Python framework for fast computation of mathematical expressions](https://mlsanity.com/paper/1605.02688/) (2016)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact](https://mlsanity.com/paper/2103.16021/) (2021)
- [DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Tools](https://mlsanity.com/paper/2203.17275/) (2022)
- [FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation](https://mlsanity.com/paper/2303.02346/) (2023)
- [DexDeform: Dexterous Deformable Object Manipulation with Human Demonstrations and Differentiable Physics](https://mlsanity.com/paper/2304.03223/) (2023)
- [SAM-RL: Sensing-Aware Model-Based Reinforcement Learning via Differentiable Physics-Based Simulation and Rendering](https://mlsanity.com/paper/2210.15185/) (2022)
- [SAGCI-System: Towards Sample-Efficient, Generalizable, Compositional, and Incremental Robot Learning](https://mlsanity.com/paper/2111.14693/) (2021)
- [Differentiable solver for time-dependent deformation problems with contact](https://mlsanity.com/paper/2205.13643/) (2022)
- [Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contact](https://mlsanity.com/paper/2309.04710/) (2023)
- [DiffXPBD : Differentiable Position-Based Simulation of Compliant Constraint Dynamics](https://mlsanity.com/paper/2301.01396/) (2023)
- [Diff-Transfer: Model-based Robotic Manipulation Skill Transfer via Differentiable Physics Simulation](https://mlsanity.com/paper/2310.04930/) (2023)

## Built on by (most cited first, 9 of 9)

- [Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulation](https://mlsanity.com/paper/2412.12089/) (2024)
- [ManiFoundation Model for General-Purpose Robotic Manipulation of Contact Synthesis with Arbitrary Objects and Robots](https://mlsanity.com/paper/2405.06964/) (2024)
- [Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Control](https://mlsanity.com/paper/2506.14186/) (2025)
- [TopoGaussian: Inferring Internal Topology Structures from Visual Clues](https://mlsanity.com/paper/2503.12343/) (2025)
- [Phys4D: Fine-Grained Physics-Consistent 4D Modeling from Video Diffusion](https://mlsanity.com/paper/2603.03485/) (2026)
- [Learning Physics-Guided Residual Dynamics for Deformable Object Simulation](https://mlsanity.com/paper/2607.13451/) (2026)
- [Learning Equivariant Neural-Augmented Object Dynamics From Few Interactions](https://mlsanity.com/paper/2605.02699/) (2026)
- [Exploring 6D Object Pose Estimation with Deformation](https://mlsanity.com/paper/2604.06720/) (2026)
- [On the Numerical Reliability of Differentiable Physics-Based Optimization for Robotic Material Manipulation](https://mlsanity.com/paper/2609.34666/) (2026)

## Abstract (arXiv)

Differentiable physics simulation provides an avenue to tackle previously intractable challenges through gradient-based optimization, thereby greatly improving the efficiency of solving robotics-related problems. To apply differentiable simulation in diverse robotic manipulation scenarios, a key challenge is to integrate various materials in a unified framework. We present SoftMAC, a differentiable simulation framework that couples soft bodies with articulated rigid bodies and clothes. SoftMAC simulates soft bodies with the continuum-mechanics-based Material Point Method (MPM). We provide a novel forecast-based contact model for MPM, which effectively reduces penetration without introducing other artifacts like unnatural rebound. To couple MPM particles with deformable and non-volumetric clothes meshes, we also propose a penetration tracing algorithm that reconstructs the signed distance field in local area. Diverging from previous works, SoftMAC simulates the complete dynamics of each modality and incorporates them into a cohesive system with an explicit and differentiable coupling mechanism. The feature empowers SoftMAC to handle a broader spectrum of interactions, such as soft bodies serving as manipulators and engaging with underactuated systems. We conducted comprehensive experiments to validate the effectiveness and accuracy of the proposed differentiable pipeline in downstream robotic manipulation applications. Supplementary materials and videos are available on our project website at https://minliu01.github.io/SoftMAC.