pith. machine review for the scientific record. sign in

arxiv: 2605.14526 · v1 · submitted 2026-05-14 · 💻 cs.GR · cs.DC· cs.NA· cs.RO· math.NA

Recognition: 2 theorem links

· Lean Theorem

DiffPhD: A Unified Differentiable Solver for Projective Heterogeneous Materials in Elastodynamics with Contact-Rich GPU-Acceleration

Shih-Yu Lai , Sung-Han Tien , Jui-I Huang , Yen-Chen Tseng , Yi-Ting Chiu , Siyuan Luo , Ziqiu Zeng , Fan Shi
show 4 more authors
Peter Yichen Chen Tiantian Liu Yu-Lun Liu Bing-Yu Chen
Authors on Pith no claims yet

Pith reviewed 2026-05-15 01:05 UTC · model grok-4.3

classification 💻 cs.GR cs.DCcs.NAcs.ROmath.NA
keywords differentiable simulationprojective dynamicsheterogeneous materialsGPU accelerationelastodynamicscontact handlinggradient accuracyhyperelasticity
0
0 comments X

The pith

DiffPhD unifies stiffness-aware projective weights, trust-region filtering, and Anderson acceleration into a single GPU pipeline that delivers exact gradients and up to 10x speedup on heterogeneous hyperelastic contact simulations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a differentiable solver for soft-body elastodynamics that embeds material heterogeneity directly into the projective dynamics formulation while keeping the backward pass exact. It combines stiffness-aware weighting, lifted eigenvalue filtering for stable hyperelastic gradients, and dual-gate Anderson acceleration to maintain convergence at stiffness ratios up to 100x. A shared sparse factorization across forward, backward, and contact steps folds in damping at no extra cost. These changes together remove the previous trade-off between speed and stability that limited differentiable simulation of real-world objects such as multi-material characters and robotic grippers.

Core claim

DiffPhD shows that a single GPU-resident sparse factor, augmented by stiffness-aware projective weights and trust-region eigenvalue filtering passed to the backward stage, together with type-II Anderson acceleration using dual-gate convergence, produces strictly accurate gradients while remaining convergent on hyperelastic heterogeneous problems with contact and stiffness contrasts up to 100x, yielding up to an order-of-magnitude wall-clock reduction versus prior differentiable projective-dynamics solvers.

What carries the argument

The unified GPU pipeline that reuses one sparse factorization for forward solve, backward gradient propagation, and contact resolution while embedding stiffness-amplified Rayleigh damping inside the same factor.

If this is right

  • End-to-end gradient-based optimization becomes feasible for shell-joint composite creatures under a single forward-backward pass.
  • Soft characters carrying stiff weapons can be optimized without solver divergence at material boundaries.
  • Soft-gripper robotic manipulation tasks can be solved with contact-rich heterogeneous models at interactive rates.
  • Heterogeneous hyperelastic scenes with large deformations remain stable without per-scene retuning of acceleration parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same factorization reuse pattern could be applied to other implicit integrators to reduce memory traffic in differentiable physics.
  • Stability at high stiffness ratios suggests the method may extend to multi-material additive manufacturing simulations without ad-hoc partitioning.
  • The approach opens a route to real-time inverse design loops for soft robotics where previous solvers were limited by either cost or fragility.

Load-bearing premise

The trust-region eigenvalue filtering and type-II Anderson acceleration with dual-gate convergence preserve both forward stability and exact gradient accuracy across all tested stiffness contrasts and contact configurations without requiring case-by-case retuning or introducing hidden bias in the backward pass.

What would settle it

Run finite-difference gradient checks on a benchmark with stiffness contrast above 100x and contact; if the reported gradients deviate beyond machine precision or the iteration count exceeds the dual-gate threshold, the claim of strict accuracy and unconditional stability fails.

Figures

Figures reproduced from arXiv: 2605.14526 by Bing-Yu Chen, Fan Shi, Jui-I Huang, Peter Yichen Chen, Shih-Yu Lai, Siyuan Luo, Sung-Han Tien, Tiantian Liu, Yen-Chen Tseng, Yi-Ting Chiu, Yu-Lun Liu, Ziqiu Zeng.

Figure 1
Figure 1. Figure 1: We present DiffPhD, a GPU-accelerated differentiable Projective Dynamics (PD) solver for heterogeneous hyperelastic [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Two consequences of material heterogeneity in Neo [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Stiffness-aware projective assembly. (a) Route het￾erogeneity through 𝑨, not the local prox. Per-element material parameters enter the global PD operator 𝑨 through projective weights 𝑤𝑒 ∝𝜇𝑒 (Eq. (12)); the local prox sees only mesh-wide scalar means. (b) Why per-element local prox fails. Mixing soft and stiff elements in the local Newton makes its prox-map Hessian element-varying: 𝒑 ∗ 𝑒 oscillates across P… view at source ↗
Figure 3
Figure 3. Figure 3: Coupled failure of heterogeneity and hyperelas￾ticity. A bi-material Armadillo (soft upper body, stiff lower body) under twist: wrist drift originates from per-element prox-map Hessians turning indefinite at soft/stiff bound￾aries, and the resulting 𝝈 ∗ ping-pong is amplified by Anderson Acceleration into mesh-level oscillation. Ad￾dressed by bounded-window AA (Sec. 4.3) and backward trust-region filtering… view at source ↗
Figure 5
Figure 5. Figure 5: Trust-region filter on the prox-map Hessian, ap [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Mesh-to-mesh deformable contact: a dominant failure mode. Penalty-based and pure-PD models leave residual error on non-convex two-body impacts—surface separation (top) or interpenetration (middle)—contaminating the backward gradients. We adopt the Signorini–Coulomb non-smooth NCP of [Zeng et al. 2025], integrated into the persistent factor pipeline (Sec. 4.6). Why no algebraic pre￾conditioner. Eq. (33) is … view at source ↗
Figure 8
Figure 8. Figure 8: Armadillo under varying stiffness contrast. The mesh is partitioned into three height-stacked sub-regions whose [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Crab pull-up: homogeneous vs. heterogeneous re [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Crab pull-up: differentiable solver comparison. From left to right: initial state, FEM (Newton-NH), Subspace [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Gatorman: robust mesh-to-mesh contact. A com [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Heterogeneous codimensional contact. We sim [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Bouncing Ball system identification: homogeneous vs. heterogeneous variants. Three rows show three time instants [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 16
Figure 16. Figure 16: Bunny inverse design. The initial guess (left) [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 15
Figure 15. Figure 15: Plant system identification: convergence curves. [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 18
Figure 18. Figure 18: Routing Tendon: muscle-driven initial-state op [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Torus locomotion: trajectory optimisation. The [PITH_FULL_IMAGE:figures/full_fig_p019_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Real-to-Sim alignment for a soft-contact manipulation pipeline. [PITH_FULL_IMAGE:figures/full_fig_p020_20.png] view at source ↗
read the original abstract

Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with heterogeneous materials with extreme stiffness contrasts, hyperelasticity under large deformations, and contact-rich interactions, which are common scenarios in the real world. We present DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework for heterogeneous materials that tackles these intertwined challenges simultaneously. Our key insight is a careful integration of: (i) stiffness-aware projective weights to embed heterogeneity into the global system; (ii) trust-region eigenvalue filtering lifted to the backward pass for stable hyperelastic gradients and a type-II Anderson Acceleration scheme with dual-gate convergence to stabilize forward iteration under large stiffness contrasts; and (iii) a unified GPU pipeline that reuses a single sparse factor across forward, backward, and contact computations, with stiffness-amplified Rayleigh damping folded into the same factor for heterogeneity-aware dissipation at zero recurring cost. DiffPhD achieves strict gradient accuracy while delivering up to an order-of-magnitude speedup over prior differentiable solvers on heterogeneous, hyperelastic, contact-rich benchmarks. Crucially, this speedup does not come at the cost of stability: DiffPhD remains convergent on stiffness contrasts up to 100x where prior PD solvers degrade. This unlocks end-to-end gradient-based optimization on regimes previously bottlenecked by either solver fragility or per-iteration cost -- shell--joint composite creatures, soft characters wielding stiff weapons, and soft-gripper robotic manipulation -- all handled within a single forward--backward pass.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper presents DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework for simulating heterogeneous elastodynamic materials under large deformations and contact. It incorporates stiffness-aware projective weights, trust-region eigenvalue filtering lifted to the backward pass, type-II Anderson acceleration with dual-gate convergence, and a single sparse factor reused across forward, backward, and contact steps (with stiffness-amplified Rayleigh damping). The central claims are strict (exact) gradient accuracy through the full pipeline, up to an order-of-magnitude speedup over prior differentiable solvers, and stable convergence on stiffness contrasts up to 100x where earlier PD methods degrade, enabling end-to-end optimization on previously intractable benchmarks such as shell-joint composites and soft-gripper manipulation.

Significance. If the strict gradient accuracy and stability claims hold without hidden approximations, the work would be a meaningful advance for differentiable physics in graphics and robotics. It directly targets the practical bottlenecks of heterogeneity, hyperelasticity, and contact that limit existing differentiable PD solvers, while delivering both speed and a reusable GPU factorization. The unified pipeline and zero-recurring-cost damping are particularly attractive for downstream tasks such as system identification and trajectory optimization.

major comments (2)
  1. [Abstract and §3 (backward pass / acceleration)] Abstract and method overview: the claim of 'strict gradient accuracy' through the full forward-backward pipeline is load-bearing for the paper's contribution. The trust-region eigenvalue filtering (lifted to the backward pass) and type-II Anderson acceleration with dual-gate convergence are non-smooth operations that alter the iteration operator. The manuscript must explicitly derive or verify that the backward pass computes the exact adjoint (or a provably correct subgradient) of the filtered forward map at every active filter location and across all reported stiffness contrasts; otherwise the accuracy claim reduces to an approximation.
  2. [§4 (experiments)] §4 (experiments): the reported stability on 100x stiffness contrasts and the order-of-magnitude speedups must be accompanied by explicit verification that the eigenvalue filter remains inactive (or is exactly differentiated) on the evaluated benchmarks. Without such verification or error-bar reporting on gradient accuracy (e.g., finite-difference checks on the full pipeline), the tension between stabilization and exact differentiability remains unresolved.
minor comments (2)
  1. [§3] Notation for the dual-gate convergence criterion and the stiffness-amplified Rayleigh damping should be introduced with a short equation or pseudocode block to avoid ambiguity when the same sparse factor is reused.
  2. [Figures in §4] Figure captions for the heterogeneous benchmarks should explicitly state the stiffness contrast ratios and contact configurations used, so readers can directly map results to the 100x claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The two major comments both center on rigorously substantiating the strict gradient accuracy claim in the presence of non-smooth stabilization mechanisms. We address each point below and commit to revisions that supply the requested derivations and verifications.

read point-by-point responses

  1. Referee: [Abstract and §3 (backward pass / acceleration)] Abstract and method overview: the claim of 'strict gradient accuracy' through the full forward-backward pipeline is load-bearing for the paper's contribution. The trust-region eigenvalue filtering (lifted to the backward pass) and type-II Anderson acceleration with dual-gate convergence are non-smooth operations that alter the iteration operator. The manuscript must explicitly derive or verify that the backward pass computes the exact adjoint (or a provably correct subgradient) of the filtered forward map at every active filter location and across all reported stiffness contrasts; otherwise the accuracy claim reduces to an approximation.

    Authors: We agree that an explicit derivation is required. In the revision we will add a new subsection in §3 that derives the adjoint of the trust-region eigenvalue filter when lifted to the backward pass, showing that it yields the exact subgradient at every active filter location. We will also prove that the dual-gate Anderson acceleration does not alter the fixed-point operator in a way that invalidates the adjoint. These derivations will be accompanied by finite-difference verification across the full range of stiffness contrasts reported in the paper. revision: yes

  2. Referee: [§4 (experiments)] §4 (experiments): the reported stability on 100x stiffness contrasts and the order-of-magnitude speedups must be accompanied by explicit verification that the eigenvalue filter remains inactive (or is exactly differentiated) on the evaluated benchmarks. Without such verification or error-bar reporting on gradient accuracy (e.g., finite-difference checks on the full pipeline), the tension between stabilization and exact differentiability remains unresolved.

    Authors: We accept this requirement. The revised §4 will include: (i) per-benchmark statistics on eigenvalue-filter activation rates for all stiffness contrasts, (ii) finite-difference error bars (mean and max relative error) for the complete forward-backward pipeline on representative heterogeneous and contact-rich examples, and (iii) explicit confirmation that the reported speedups and stability results hold under exact differentiation. These additions will directly resolve the noted tension. revision: yes

Circularity Check

0 steps flagged

Extends projective dynamics with new stabilization and GPU components; no reduction of claims to self-fit or definitional loops

full rationale

The derivation chain introduces stiffness-aware projective weights, trust-region eigenvalue filtering lifted to the backward pass, type-II Anderson acceleration with dual-gate convergence, and a unified sparse-factor GPU pipeline. These are presented as independent engineering choices that preserve strict gradient accuracy on the stated benchmarks. No equation or claim reduces a reported prediction or accuracy result to a fitted parameter on the same data, nor does any uniqueness theorem collapse to a self-citation whose content is unverified. Self-citations to prior PD/DiffPD work are present but serve only as the base solver; the new stabilization and performance claims remain externally falsifiable on the heterogeneous contact benchmarks. This yields a minor self-citation score without load-bearing circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities. The central claims rest on the unstated assumption that the listed numerical techniques integrate without side effects on the underlying elastodynamic equations.

pith-pipeline@v0.9.0 · 5661 in / 1207 out tokens · 34727 ms · 2026-05-15T01:05:11.385330+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

145 extracted references · 145 canonical work pages · 2 internal anchors

  1. [1]

    The Computational Geometry Algorithms Library , author =

    work page

  2. [2]

    Menelaos Karavelas , subtitle =

    work page

  3. [3]

    The Computational Geometry Algorithms Library , subtitle =

    Menelaos Karavelas , editor =. The Computational Geometry Algorithms Library , subtitle =

    work page

  4. [4]

    The Parmap library , author =

    work page

  5. [5]

    Christopher Anderson and Sophia Drossopoulou , title =

    work page

  6. [6]

    ACM Trans

    Li, Pei-Xuan and Chang, Yu-En and Wei, Ming-Chun and Hsieh, Hsun-Ping , title =. ACM Trans. Manage. Inf. Syst. , month =. 2024 , publisher =

    work page 2024

  7. [7]

    Dosovitskiy, Alexey and Beyer, Lucas and Kolesnikov, Alexander and Weissenborn, Dirk and Zhai, Xiaohua and Unterthiner, Thomas and Dehghani, Mostafa and Minderer, Matthias and Heigold, Georg and Gelly, Sylvain and Uszkoreit, Jakob and Houlsby, Neil , month = jun, year =. An. doi:10.48550/arXiv.2010.11929 , urldate =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2010.11929 2010

  8. [8]

    Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , pages =

    Chen, Tianqi and Guestrin, Carlos , title =. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , pages =. 2016 , isbn =

    work page 2016

  9. [9]

    Feurer, K

    Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning , author =. arXiv:2007.04074 [cs.LG] , year =

    work page arXiv 2007

  10. [10]

    Zimmer, Lucas and Lindauer, Marius and Hutter, Frank , pages =

    work page

  11. [11]

    2014 , issue_date =

    Bouaziz, Sofien and Martin, Sebastian and Liu, Tiantian and Kavan, Ladislav and Pauly, Mark , title =. 2014 , issue_date =. doi:10.1145/2601097.2601116 , journal =

    work page doi:10.1145/2601097.2601116 2014

  12. [12]

    Seminal Graphics Papers: Pushing the Boundaries, Volume 2 , articleno =

    Bouaziz, Sofien and Martin, Sebastian and Liu, Tiantian and Kavan, Ladislav and Pauly, Mark , title =. Seminal Graphics Papers: Pushing the Boundaries, Volume 2 , articleno =. 2023 , isbn =

    work page 2023

  13. [13]

    2022 , issue_date =

    Wu, Botao and Wang, Zhendong and Wang, Huamin , title =. 2022 , issue_date =. doi:10.1145/3528223.3530085 , journal =

    work page doi:10.1145/3528223.3530085 2022

  14. [14]

    Fischer , title =

    A. Fischer , title =. Optimization , volume =. 1992 , publisher =. doi:10.1080/02331939208843795 , URL =

    work page doi:10.1080/02331939208843795 1992

  15. [15]

    1997 , url =

    Karypis, George and Kumar, Vipin , title =. 1997 , url =

    work page 1997

  16. [16]

    2021 , issue_date =

    Du, Tao and Wu, Kui and Ma, Pingchuan and Wah, Sebastien and Spielberg, Andrew and Rus, Daniela and Matusik, Wojciech , title =. 2021 , issue_date =. doi:10.1145/3490168 , journal =

    work page doi:10.1145/3490168 2021

  17. [17]

    2025 , issue_date =

    Zeng, Ziqiu and Luo, Siyuan and Shi, Fan and Zhang, Zhongkai , title =. 2025 , issue_date =. doi:10.1145/3730834 , journal =

    work page doi:10.1145/3730834 2025

  18. [18]

    Atti della Societ\`a Italiana per il Progresso delle Scienze , volume =

    Signorini, Antonio , title =. Atti della Societ\`a Italiana per il Progresso delle Scienze , volume =

    work page

  19. [19]

    and Ni, Peng , title =

    Walker, Homer F. and Ni, Peng , title =. 2011 , issue_date =. doi:10.1137/10078356X , journal =

    work page doi:10.1137/10078356x 2011

  20. [20]

    and Levin, David I.W

    Trusty, Ty and Benchekroun, Otman and Grinspun, Eitan and Kaufman, Danny M. and Levin, David I.W. , title =. 2023 , isbn =. doi:10.1145/3610548.3618220 , booktitle =

    work page doi:10.1145/3610548.3618220 2023

  21. [21]

    and Zheng, Changxi , title =

    Chen, Honglin and Liu, Hsueh-Ti Derek and Jacobson, Alec and Levin, David I.W. and Zheng, Changxi , title =. 2024 , isbn =. doi:10.1145/3680528.3687650 , booktitle =

    work page doi:10.1145/3680528.3687650 2024

  22. [22]

    Proceedings of the 39th International Conference on Machine Learning , pages =

    Fast Aquatic Swimmer Optimization with Differentiable Projective Dynamics and Neural Network Hydrodynamic Models , author =. Proceedings of the 39th International Conference on Machine Learning , pages =. 2022 , editor =

    work page 2022

  23. [23]

    International Conference on Machine Learning , year=

    Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics , author=. International Conference on Machine Learning , year=

    work page

  24. [24]

    SIGGRAPH , year=

    Geometric Contact Potential , author=. SIGGRAPH , year=

    work page

  25. [25]

    Modi, Vismay and Sharp, Nicholas and Perel, Or and Sueda, Shinjiro and Levin, David I. W. , title =. 2024 , issue_date =. doi:10.1145/3658184 , journal =

    work page doi:10.1145/3658184 2024

  26. [26]

    International Conference on Learning Representations (ICLR) , year =

    Li, Sizhe and Huang, Zhiao and Du, Tao and Su, Hao and Tenenbaum, Joshua and Gan, Chuang , title =. International Conference on Learning Representations (ICLR) , year =

    work page

  27. [27]

    2009 , issue_date =

    Kikuuwe, Ryo and Tabuchi, Hiroaki and Yamamoto, Motoji , title =. 2009 , issue_date =. doi:10.1145/1477926.1477934 , journal =

    work page doi:10.1145/1477926.1477934 2009

  28. [28]

    1997 , publisher=

    Non-linear elastic deformations , author=. 1997 , publisher=

    work page 1997

  29. [29]

    ACM Transactions on Graphics (TOG) , volume=

    Stable neo-hookean flesh simulation , author=. ACM Transactions on Graphics (TOG) , volume=. 2018 , publisher=

    work page 2018

  30. [30]

    ACM SIGGRAPH 2022 Courses , pages=

    Dynamic deformables: implementation and production practicalities (now with code!) , author=. ACM SIGGRAPH 2022 Courses , pages=

    work page 2022

  31. [31]

    , author=

    Isotropic ARAP Energy Using Cauchy-Green Invariants. , author=. ACM Trans. Graph. , volume=

    work page

  32. [32]

    ACM SIGGRAPH 2024 Conference Papers , pages=

    Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton , author=. ACM SIGGRAPH 2024 Conference Papers , pages=

    work page 2024

  33. [33]

    Journal of Applied Physics , volume=

    Torsion of a rubber cylinder , author=. Journal of Applied Physics , volume=. 1947 , publisher=

    work page 1947

  34. [34]

    Journal of applied physics , volume=

    A theory of large elastic deformation , author=. Journal of applied physics , volume=

    work page

  35. [35]

    Parameters , volume=

    Hyperelastic Mooney-Rivlin model: determination and physical interpretation of material constants , author=. Parameters , volume=

    work page

  36. [36]

    2017 , issue_date =

    Liu, Tiantian and Bouaziz, Sofien and Kavan, Ladislav , title =. 2017 , issue_date =. doi:10.1145/3072959.2990496 , journal =

    work page doi:10.1145/3072959.2990496 2017

  37. [37]

    Journal of Visual Communication and Image Representation , volume=

    Position based dynamics , author=. Journal of Visual Communication and Image Representation , volume=. 2007 , publisher=

    work page 2007

  38. [38]

    and Li, Jie and Narain, Rahul , journal=

    Overby, Matthew and Brown, George E. and Li, Jie and Narain, Rahul , journal=. ADMM Projective Dynamics: Fast Simulation of Hyperelastic Models with Dynamic Constraints , year=. doi:10.1109/TVCG.2017.2730875 , ISSN=

    work page doi:10.1109/tvcg.2017.2730875 2017

  39. [39]

    , title =

    Narain, Rahul and Overby, Matthew and Brown, George E. , title =. Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation , pages =. 2016 , isbn =

    work page 2016

  40. [40]

    and Fulton, L

    Modi, V. and Fulton, L. and Jacobson, A. and Sueda, S. and Levin, D.I.W. , title =. Computer Graphics Forum , volume =. doi:https://doi.org/10.1111/cgf.14185 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.14185 , year =

    work page doi:10.1111/cgf.14185

  41. [41]

    Pacific Graphics Conference Papers, Posters, and Demos , editor =

    Cai, Youshuai and Li, Chen and Song, Haichuan and Xie, Youchen and Wang, ChangBo , year =. Pacific Graphics Conference Papers, Posters, and Demos , editor =

    work page

  42. [42]

    Proceedings of IEEE International Conference on Robotics and Automation (ICRA) , year=

    ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics , author=. Proceedings of IEEE International Conference on Robotics and Automation (ICRA) , year=

    work page

  43. [43]

    International Conference on Learning Representations , year=

    DiffTaichi: Differentiable Programming for Physical Simulation , author=. International Conference on Learning Representations , year=

    work page

  44. [44]

    Symposium on Computer Animation , editor =

    Teran, Joseph and Sifakis, Eftychios and Irving, Geoffrey and Fedkiw, Ronald , year =. Symposium on Computer Animation , editor =

    work page

  45. [45]

    2024 , issue_date =

    Lu, Zixuan and He, Xiaowei and Guo, Yuzhong and Liu, Xuehui and Wang, Huamin , title =. 2024 , issue_date =. doi:10.1109/TVCG.2023.3271511 , journal =

    work page doi:10.1109/tvcg.2023.3271511 2024

  46. [46]

    and Coros, Stelian , title =

    Hahn, David and Banzet, Pol and Bern, James M. and Coros, Stelian , title =. 2019 , issue_date =. doi:10.1145/3355089.3356548 , journal =

    work page doi:10.1145/3355089.3356548 2019

  47. [47]

    ADD: analytically differentiable dynamics for multi-body systems with frictional contact , year =

    Geilinger, Moritz and Hahn, David and Zehnder, Jonas and B\". ADD: analytically differentiable dynamics for multi-body systems with frictional contact , year =. doi:10.1145/3414685.3417766 , journal =

    work page doi:10.1145/3414685.3417766

  48. [48]

    2022 , issue_date =

    Li, Yifei and Du, Tao and Wu, Kui and Xu, Jie and Matusik, Wojciech , title =. 2022 , issue_date =. doi:10.1145/3527660 , journal =

    work page doi:10.1145/3527660 2022

  49. [49]

    Differentiable Cloth Simulation for Inverse Problems , url =

    Liang, Junbang and Lin, Ming and Koltun, Vladlen , booktitle =. Differentiable Cloth Simulation for Inverse Problems , url =

    work page

  50. [50]

    , title =

    Qiao, Yi-Ling and Liang, Junbang and Koltun, Vladlen and Lin, Ming C. , title =. Proceedings of the 37th International Conference on Machine Learning , articleno =. 2020 , publisher =

    work page 2020

  51. [51]

    International Conference on Learning Representations , year=

    Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids , author=. International Conference on Learning Representations , year=

    work page

  52. [52]

    , title =

    Sanchez-Gonzalez, Alvaro and Godwin, Jonathan and Pfaff, Tobias and Ying, Rex and Leskovec, Jure and Battaglia, Peter W. , title =. Proceedings of the 37th International Conference on Machine Learning , articleno =. 2020 , publisher =

    work page 2020

  53. [53]

    Soft robotics , volume=

    Dynamic simulation of soft multimaterial 3d-printed objects , author=. Soft robotics , volume=. 2014 , publisher=

    work page 2014

  54. [54]

    SOFA - an Open Source Framework for Medical Simulation , volume =

    Allard, Jeremie and Cotin, St. SOFA - an Open Source Framework for Medical Simulation , volume =. 2007 , month =

    work page 2007

  55. [55]

    ALIFE XV, the fifteenth international conference on the synthesis and simulation of living systems, late breaking proceedings , volume=

    Evolving swimming soft-bodied creatures , author=. ALIFE XV, the fifteenth international conference on the synthesis and simulation of living systems, late breaking proceedings , volume=

    work page

  56. [56]

    Material properties affect evolution's ability to exploit morphological computation in growing soft-bodied creatures , doi =

    Corucci, Francesco and Cheney, Nick and Lipson, Hod and Laschi, Cecilia and Bongard, Josh , year =. Material properties affect evolution's ability to exploit morphological computation in growing soft-bodied creatures , doi =

    work page

  57. [57]

    2013 , isbn =

    Cheney, Nick and MacCurdy, Robert and Clune, Jeff and Lipson, Hod , title =. 2013 , isbn =. doi:10.1145/2463372.2463404 , booktitle =

    work page doi:10.1145/2463372.2463404 2013

  58. [58]

    2018 , issue_date =

    Lee, Seunghwan and Yu, Ri and Park, Jungnam and Aanjaneya, Mridul and Sifakis, Eftychios and Lee, Jehee , title =. 2018 , issue_date =. doi:10.1145/3197517.3201330 , journal =

    work page doi:10.1145/3197517.3201330 2018

  59. [59]

    Real-Time subspace integration for St

    Barbi. Real-Time subspace integration for St. Venant-Kirchhoff deformable models , year =. doi:10.1145/1073204.1073300 , journal =

    work page doi:10.1145/1073204.1073300

  60. [60]

    2019 , MONTH = Jan, DOI =

    Thieffry, Maxime and Kruszewski, Alexandre and Duriez, Christian and Guerra, Thierry-Marie , URL =. 2019 , MONTH = Jan, DOI =

    work page 2019

  61. [61]

    , author=

    Trajectory Optimization for Cable-Driven Soft Robot Locomotion. , author=. Robotics: Science and Systems , volume=

    work page

  62. [62]

    2019 , issue_date =

    Min, Sehee and Won, Jungdam and Lee, Seunghwan and Park, Jungnam and Lee, Jehee , title =. 2019 , issue_date =. doi:10.1145/3355089.3356497 , journal =

    work page doi:10.1145/3355089.3356497 2019

  63. [63]

    Learning-In-The-Loop Optimization: End-To-End Control And Co-Design Of Soft Robots Through Learned Deep Latent Representations , url =

    Spielberg, Andrew and Zhao, Allan and Hu, Yuanming and Du, Tao and Matusik, Wojciech and Rus, Daniela , booktitle =. Learning-In-The-Loop Optimization: End-To-End Control And Co-Design Of Soft Robots Through Learned Deep Latent Representations , url =

    work page

  64. [64]

    2024 , issue_date =

    Huang, Zizhou and Tozoni, Davi Colli and Gjoka, Arvi and Ferguson, Zachary and Schneider, Teseo and Panozzo, Daniele and Zorin, Denis , title =. 2024 , issue_date =. doi:10.1145/3657648 , journal =

    work page doi:10.1145/3657648 2024

  65. [65]

    2024 , isbn =

    Benchekroun, Otman and Xie, Kaixiang and Liu, Hsueh-Ti Derek and Grinspun, Eitan and Andrews, Sheldon and Zordan, Victor , title =. 2024 , isbn =. doi:10.1145/3680528.3687638 , booktitle =

    work page doi:10.1145/3680528.3687638 2024

  66. [66]

    2024 , issue_date =

    Trusty, Ty and Fei, Yun (Raymond) and Levin, David and Kaufman, Danny , title =. 2024 , issue_date =. doi:10.1145/3687946 , journal =

    work page doi:10.1145/3687946 2024

  67. [67]

    2025 , issue_date =

    Benchekroun, Otman and Grinspun, Eitan and Chiaramonte, Maurizio and Etter, Philip Allen , title =. 2025 , issue_date =. doi:10.1145/3763310 , journal =

    work page doi:10.1145/3763310 2025

  68. [68]

    1984 , publisher=

    Non-linear Elastic Deformations , author=. 1984 , publisher=

    work page 1984

  69. [69]

    , title =

    Mooney, M. , title =. Journal of Applied Physics , volume =. 1940 , month =. doi:10.1063/1.1712836 , url =

    work page doi:10.1063/1.1712836 1940

  70. [70]

    Rivlin, R. S. , title =. Journal of Applied Physics , volume =. 1947 , month =. doi:10.1063/1.1697674 , url =

    work page doi:10.1063/1.1697674 1947

  71. [71]

    Venkateswara , title =

    Kumar, Nomesh and Rao, V. Venkateswara , title =. MIT International Journal of Mechanical Engineering , year =

    work page

  72. [72]

    2018 , issue_date =

    Smith, Breannan and Goes, Fernando De and Kim, Theodore , title =. 2018 , issue_date =. doi:10.1145/3180491 , journal =

    work page doi:10.1145/3180491 2018

  73. [73]

    2020 , isbn =

    Kim, Theodore and Eberle, David , title =. 2020 , isbn =. doi:10.1145/3388769.3407490 , booktitle =

    work page doi:10.1145/3388769.3407490 2020

  74. [74]

    2019 , publisher=

    Practical optimization , author=. 2019 , publisher=

    work page 2019

  75. [75]

    2006 , publisher=

    Numerical optimization , author=. 2006 , publisher=

    work page 2006

  76. [76]

    2016 , issue_date =

    Fu, Xiao-Ming and Liu, Yang , title =. 2016 , issue_date =. doi:10.1145/2980179.2980231 , journal =

    work page doi:10.1145/2980179.2980231 2016

  77. [77]

    SIAM Journal on Optimization , volume =

    Paternain, Santiago and Mokhtari, Aryan and Ribeiro, Alejandro , title =. SIAM Journal on Optimization , volume =. 2019 , doi =

    work page 2019

  78. [78]

    2023 , eprint=

    Pitfalls of Projection: A study of Newton-type solvers for incremental potentials , author=. 2023 , eprint=

    work page 2023

  79. [79]

    2023 , issue_date =

    Lan, Lei and Li, Minchen and Jiang, Chenfanfu and Wang, Huamin and Yang, Yin , title =. 2023 , issue_date =. doi:10.1145/3592104 , journal =

    work page doi:10.1145/3592104 2023

  80. [80]

    2024 , isbn =

    Shen, Xing and Cai, Runyuan and Bi, Mengxiao and Lv, Tangjie , title =. 2024 , isbn =. doi:10.1145/3641519.3657490 , booktitle =

    work page doi:10.1145/3641519.3657490 2024

Showing first 80 references.