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DiffPD: Differentiable Projective Dynamics

arXiv 2101.05917 ↗First posted 15 Jan 2021cs.LG cs.GRcited by 62

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Abstract (arXiv)

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using explicit time-stepping schemes require tiny time steps to avoid numerical instabilities in gradient computation, and simulators using implicit time integration typically compute gradients by employing the adjoint method and solving the expensive linearized dynamics. Inspired by Projective Dynamics (PD), we present Differentiable Projective Dynamics (DiffPD), an efficient differentiable soft-body simulator based on PD with implicit time integration. The key idea in DiffPD is to speed up backpropagation by exploiting the prefactorized Cholesky decomposition in forward PD simulation. In terms of contact handling, DiffPD supports two types of contacts: a penalty-based model describing contact and friction forces and a complementarity-based model enforcing non-penetration conditions and static friction. We evaluate the performance of DiffPD and observe it is 4-19 times faster compared with the standard Newton's method in various applications including system identification, inverse design problems, trajectory optimization, and closed-loop control. We also apply DiffPD in a reality-to-simulation (real-to-sim) example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.

Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). Builds on 10 of its 59 references that are in the map. First posted on arXiv 15 Jan 2021.

Builds on

10 of 59 references.

References · 10

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2017Proximal Policy Optimization Algorithmscited by 14,441
  3. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  4. 2019DiffTaichi: Differentiable Programming for Physical Simulationcited by 248
  5. 2018Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluidscited by 219
  6. 2020Learning to Control PDEs with Differentiable Physicscited by 131
  7. 2016A Differentiable Physics Engine for Deep Learning in Roboticscited by 107
  8. 2018ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Roboticscited by 98
  9. 2020Scalable Differentiable Physics for Learning and Controlcited by 72
  10. 2018SPNets: Differentiable Fluid Dynamics for Deep Neural Networkscited by 62

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 6; 2023: 12; 2024: 13; 2025: 16; 2026: 14.

62 papers.

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  1. 2022Accelerated Policy Learning with Parallel Differentiable Simulationcited by 92
  2. 2024Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussianscited by 92
  3. 2024LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discoverycited by 82
  4. 2021DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contactcited by 64
  5. 2023Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamicscited by 56
  6. 2024GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulationcited by 48
  7. 2022DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Toolscited by 44
  8. 2023DiffAvatar: Simulation-Ready Garment Optimization with Differentiable Simulationcited by 40
  9. 2023DiffuseBot: Breeding Soft Robots With Physics-Augmented Generative Diffusion Modelscited by 30
  10. 2022RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimationcited by 29
  11. 2023DexDeform: Dexterous Deformable Object Manipulation with Human Demonstrations and Differentiable Physicscited by 23
  12. 2022SAM-RL: Sensing-Aware Model-Based Reinforcement Learning via Differentiable Physics-Based Simulation and Renderingcited by 22
38 more
  1. 2023ClothesNet: An Information-Rich 3D Garment Model Repository with Simulated Clothes Environmentcited by 22
  2. 2025Particle-Grid Neural Dynamics for Learning Deformable Object Models from RGB-D Videoscited by 22
  3. 2025Dress-1-to-3: Single Image to Simulation-Ready 3D Outfit with Diffusion Prior and Differentiable Physicscited by 19
  4. 2024Adaptive Horizon Actor-Critic for Policy Learning in Contact-Rich Differentiable Simulationcited by 18
  5. 2025Vid2Sim: Generalizable, Video-based Reconstruction of Appearance, Geometry and Physics for Mesh-free Simulationcited by 18
  6. 2024Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulationcited by 14
  7. 2025VFXMaster: Unlocking Dynamic Visual Effect Generation via In-Context Learningcited by 12
  8. 2025UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulationcited by 11
  9. 2024NeuralFluid: Neural Fluidic System Design and Control with Differentiable Simulationcited by 10
  10. 2023SoftMAC: Differentiable Soft Body Simulation with Forecast-based Contact Model and Two-way Coupling with Articulated Rigid Bodies and Clothescited by 9
  11. 2023Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contactcited by 7
  12. 2023Differentiable Visual Computing for Inverse Problems and Machine Learningcited by 7
  13. 2025MASIV: Toward Material-Agnostic System Identification from Videoscited by 7
  14. 2025Seeing the Wind from a Falling Leafcited by 7
  15. 2022Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?cited by 6
  16. 2023DiffVL: Scaling Up Soft Body Manipulation using Vision-Language Driven Differentiable Physicscited by 6
  17. 2026MOSIV: Multi-Object System Identification from Videoscited by 6
  18. 2023Improving Gradient Computation for Differentiable Physics Simulation with Contactscited by 5
  19. 2024Implicit Neural Representation for Physics-driven Actuated Soft Bodiescited by 5
  20. 2025ParticleGS: Learning Neural Gaussian Particle Dynamics from Videos for Prior-free Physical Motion Extrapolationcited by 5
  21. 2026ReconPhys: Reconstruct Appearance and Physical Attributes from Single Videocited by 5
  22. 2022Differentiable Analog Quantum Computing for Optimization and Controlcited by 4
  23. 2024RayProNet: A Neural Point Field Framework for Radio Propagation Modeling in 3D Environmentscited by 4
  24. 2025Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challengescited by 4
  25. 2024An Implicit Physical Face Model Driven by Expression and Stylecited by 3
  26. 2024Learning Object Properties Using Robot Proprioception via Differentiable Robot-Object Interactioncited by 3
  27. 2024Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domainscited by 3
  28. 2025Differentiable Information Enhanced Model-Based Reinforcement Learningcited by 3
  29. 2025Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisionscited by 2
  30. 2025TopoGaussian: Inferring Internal Topology Structures from Visual Cluescited by 2
  31. 2025FOLIAGE: Towards Physical Intelligence World Models Via Unbounded Surface Evolutioncited by 2
  32. 2026NeuROK: Generative 4D Neural Object Kinematicscited by 2
  33. 2026Learning Physics-Guided Residual Dynamics for Deformable Object Simulationcited by 2
  34. 2023Diff-Transfer: Model-based Robotic Manipulation Skill Transfer via Differentiable Physics Simulationcited by 1
  35. 2024Mastering Contact-rich Tasks by Combining Soft and Rigid Robotics with Imitation Learningcited by 1
  36. 2025Accelerated Learning with Linear Temporal Logic using Differentiable Simulationcited by 1
  37. 2025Neural Modular Physics for Elastic Simulationcited by 1
  38. 2026Differentiate the Solver, Not the Equation: Reverse-Sweep Adjoints for Block Implicit Simulationcited by 1

50 most cited of 62 All 62 (JSON)