“Differentiable solver for time-dependent deformation problems with contact”
Conference:
Type(s):
Title:
- Differentiable solver for time-dependent deformation problems with contact
Presenter(s)/Author(s):
Abstract:
We introduce a general differentiable solver for time-dependent deformation problems to solve PDE-constrained optimizations. It supports differentiation with respect to all physical parameters involved, including shape, material parameters, friction coefficient, and initial conditions. Our analytically derived formulation is efficient, with a small overhead over the forward simulation.
References:
[1]
Christie Alappat, Achim Basermann, Alan R. Bishop, Holger Fehske, Georg Hager, Olaf Schenk, Jonas Thies, and Gerhard Wellein. 2020. A recursive algebraic coloring technique for hardware-efficient symmetric sparse matrix-vector multiplication. ACM Trans. Parallel Comput. 7, 3, Article 19 (June2020), 37 pages.
[2]
Gr?goire Allaire, Charles Dapogny, and Fran?ois Jouve. 2021. Chapter 1 – Shape and topology optimization. In Geometric Partial Differential Equations – Part II , Andrea Bonito and Ricardo H. Nochetto (Eds.). Handbook of Numerical Analysis, Vol. 22. Elsevier, 1?132. DOI:
[3]
M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells. 2015. The FEniCS project version 1.5. Archive of Numerical Software 3 (2015). DOI:
[4]
Moritz B?cher, Espen Knoop, and Christian Schumacher. 2021. Design and control of soft robots using differentiable simulation. Current Robotics Reports (2021), 1?11.
[5]
Pierre Baque, Edoardo Remelli, Fran?ois Fleuret, and Pascal Fua. 2018. Geodesic convolutional shape optimization. In International Conference on Machine Learning . PMLR, 472?481.
[6]
Ted Belytschko, Wing Kam Liu, and Brian Moran. 2000. Nonlinear Finite Elements for Continua and Structures . John Wiley & Sons, Ltd.
[7]
P. Beremlijski, J. Haslinger, J. Outrata, and R. Path?. 2014. Shape optimization in contact problems with Coulomb friction and a solution-dependent friction coefficient. SIAM Journal on Control and Optimization 52, 5 (Jan.2014), 3371?3400. DOI:
[8]
James Bern, Pol Banzet, Roi Poranne, and Stelian Coros. 2019. Trajectory optimization for cable-driven soft robot locomotion. In Robotics: Science and Systems XV , Vol. 1. Robotics: Science and Systems Foundation. DOI:
[9]
James M. Bern, Yannick Schnider, Pol Banzet, Nitish Kumar, and Stelian Coros. 2020. Soft robot control with a learned differentiable model. In 2020 3rd IEEE International Conference on Soft Robotics (RoboSoft ?20) . IEEE, 417?423. DOI:
[10]
C. H. Bischof and H. M. B?cker. 2000. Computing derivatives of computer programs. In Modern Methods and Algorithms of Quantum Chemistry: Proceedings, Second Edition , J. Grotendorst (Ed.). NIC Series, Vol. 3. NIC-Directors, J?lich, 315?327. http://hdl.handle.net/2128/6053
[11]
Matthias Bollh?fer, Aryan Eftekhari, Simon Scheidegger, and Olaf Schenk. 2019. Large-scale sparse inverse covariance matrix estimation. SIAM Journal on Scientific Computing 41, 1 (2019), A380?A401. DOI: arXiv:https://doi.org/10.1137/17M1147615
[12]
Matthias Bollh?fer, Olaf Schenk, Radim Janalik, Steve Hamm, and Kiran Gullapalli. 2020. State-of-the-art sparse direct solvers. (2020), 3?33.
[13]
Robert Bridson, Ronald Fedkiw, and John Anderson. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. on Graph. 21 (052002).
[14]
Bernard Brogliato. 1999. Nonsmooth Mechanics . Springer-Verlag.
[15]
George E. Brown, Matthew Overby, Zahra Forootaninia, and Rahul Narain. 2018. Accurate dissipative forces in optimization integrators. ACM Trans. Graph. 37, 6, Article 282 (Dec.2018), 14 pages. DOI:
[16]
Michael B. Chang, Tomer Ullman, Antonio Torralba, and Joshua B. Tenenbaum. 2016. A compositional object-based approach to learning physical dynamics. arXiv preprint arXiv:1612.00341 (2016).
[17]
Bicheng Chen, Nianfeng Wang, Xianmin Zhang, and Wei Chen. 2020. Design of dielectric elastomer actuators using topology optimization on electrodes. Smart Mater. Struct. 29, 7 (June2020), 075029. DOI:
[18]
Gilles Daviet, Florence Bertails-Descoubes, and Laurence Boissieux. 2011. A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics. ACM Trans. on Graph. 30 (122011).
[19]
Alban de Vaucorbeil, Vinh Phu Nguyen, Sina Sinaie, and Jian Ying Wu. 2019. Material point method after 25 years: Theory, implementation and applications. Submitted to Advances in Applied Mechanics (2019), 1.
[20]
B. Desmorat. 2007. Structural rigidity optimization with frictionless unilateral contact. International Journal of Solids and Structures 44, 3 (Feb.2007), 1132?1144. DOI:
[21]
J?rgen S. Dokken, Sebastian K. Mitusch, and Simon W. Funke. 2020. Automatic Shape Derivatives for Transient PDEs in FEniCS and Firedrake. (2020). arxiv:math.OC/2001.10058
[22]
Tao Du, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, and Wojciech Matusik. 2021. DiffPD: Differentiable projective dynamics. ACM Trans. Graph. 41, 2, Article 13 (Nov.2021), 21 pages. DOI:
[23]
Christof Eck, Jiri Jarusek, Miroslav Krbec, Jiri Jarusek, and Miroslav Krbec. 2005. Unilateral Contact Problems: Variational Methods and Existence Theorems . CRC Press. DOI:
[24]
Zachary Ferguson and others. 2020. IPC Toolkit. Retrieved from https://github.com/ipc-sim/ipc-toolkit
[25]
Zachary Ferguson, Minchen Li, Teseo Schneider, Francisca Gil-Ureta, Timothy Langlois, Chenfanfu Jiang, Denis Zorin, Danny M. Kaufman, and Daniele Panozzo. 2021. Intersection-free rigid body dynamics. ACM Transactions on Graphics (SIGGRAPH) 40, 4, Article 183 (2021).
[26]
Konstantinos Gavriil, Ruslan Guseinov, Jes?s P?rez, Davide Pellis, Paul Henderson, Florian Rist, Helmut Pottmann, and Bernd Bickel. 2020. Computational design of cold bent glass Fa?Ades. ACM Trans. Graph. 39, 6, Article 208 (Nov.2020), 16 pages. DOI:
[27]
Moritz Geilinger, David Hahn, Jonas Zehnder, Moritz B?cher, Bernhard Thomaszewski, and Stelian Coros. 2020. ADD: Analytically differentiable dynamics for multi-body systems with frictional contact. ACM Transactions on Graphics (TOG) 39, 6 (2020), 1?15.
[28]
Christophe Geuzaine and Jean-Fran?ois Remacle. 2009. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. Internat. J. Numer. Methods Engrg. 79, 11 (2009), 1309?1331. DOI: arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.2579
[29]
Andreas Griewank and Andrea Walther. 2008. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation . Vol. 105. SIAM. DOI:
[30]
Christian Hafner, Christian Schumacher, Espen Knoop, Thomas Auzinger, Bernd Bickel, and Moritz B?cher. 2019. X-CAD: Optimizing CAD models with extended finite elements. ACM Trans. Graph. 38, 6, Article 157 (Nov.2019), 15 pages. DOI:
[31]
David Hahn, Pol Banzet, James M. Bern, and Stelian Coros. 2019. Real2Sim: Visco-elastic parameter estimation from dynamic motion. ACM Trans. Graph. 38, 6, Article 236 (Nov.2019), 13 pages. DOI:
[32]
David Harmon, Etienne Vouga, Breannan Smith, Rasmus Tamstorf, and Eitan Grinspun. 2009. Asynchronous contact mechanics. In ACM Trans. on Graph. (TOG ?09) , Vol. 28. ACM.
[33]
David Harmon, Etienne Vouga, Rasmus Tamstorf, and Eitan Grinspun. 2008. Robust treatment of simultaneous collisions. SIGGRAPH (ACM Trans. on Graph.) 27, 3 (2008).
[34]
Jaroslav Haslinger, Pekka Neittaanmaki, and Timo Tiihonen. 1986. Shape optimization in contact problems based on penalization of the state inequality. Aplikace Matematiky 31, 1 (1986), 54?77. https://eudml.org/doc/15435
[35]
Eric Heiden, Miles Macklin, Yashraj S. Narang, Dieter Fox, Animesh Garg, and Fabio Ramos. 2021. DiSECt: A differentiable simulation engine for autonomous robotic cutting. In Proceedings of Robotics: Science and Systems . Virtual. DOI:
[36]
Eric Heiden, David Millard, Erwin Coumans, Yizhou Sheng, and Gaurav S. Sukhatme. 2020. NeuralSim: Augmenting differentiable simulators with neural networks. arXiv preprint arXiv:2011.04217 (2020).
[37]
J. Herskovits, A. Leontiev, G. Dias, and G. Santos. 2000. Contact shape optimization: A bilevel programming approach. Structural and Multidisciplinary Optimization 20, 3 (Nov.2000), 214?221. DOI:
[38]
Shayan Hoshyari, Hongyi Xu, Espen Knoop, Stelian Coros, and Moritz B?cher. 2019. Vibration-minimizing motion retargeting for robotic characters. ACM Trans. Graph. 38, 4 (July2019), 1?14. DOI:
[39]
Jerry Hsu, Nghia Truong, Cem Yuksel, and Kui Wu. 2022. A general two-stage initialization for sag-free deformable simulations. ACM Trans. Graph. 41, 4, Article 64 (Jul.2022), 13 pages. DOI:
[40]
Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Fredo Durand. 2019a. DiffTaichi: Differentiable programming for physical simulation. In International Conference on Learning Representations .
[41]
Yuanming Hu, Jiancheng Liu, Andrew Spielberg, Joshua B. Tenenbaum, William T. Freeman, Jiajun Wu, Daniela Rus, and Wojciech Matusik. 2019b. ChainQueen: A real-time differentiable physical simulator for soft robotics. In 2019 International Conference on Robotics and Automation (ICRA ?19) . IEEE, 6265?6271.
[42]
Yixin Hu, Teseo Schneider, Bolun Wang, Denis Zorin, and Daniele Panozzo. 2020. Fast tetrahedral meshing in the wild. ACM Trans. Graph. 39, 4, Article 117 (July2020), 18 pages. DOI:
[43]
Wenzel Jakob. 2010. Mitsuba Renderer. (2010). http://www.mitsuba-renderer.org
[44]
Krishna Murthy Jatavallabhula, Miles Macklin, Florian Golemo, Vikram Voleti, Linda Petrini, Martin Weiss, Breandan Considine, Jerome Parent-Levesque, Kevin Xie, Kenny Erleben, Liam Paull, Florian Shkurti, Derek Nowrouzezahrai, and Sanja Fidler. 2021. gradSim: Differentiable simulation for system identification and visuomotor control. International Conference on Learning Representations (ICLR) (2021). https://openreview.net/forum?id=c_E8kFWfhp0
[45]
Zhongshi Jiang, Teseo Schneider, Denis Zorin, and Daniele Panozzo. 2020. Bijective projection in a shell. ACM Trans. Graph. 39, 6, Article 247 (Nov.2020), 18 pages. DOI:
[46]
Noboru Kikuchi and John Tinsley Oden. 1988. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods . SIAM Studies in App. and Numer. Math., Vol. 8. Society for Industrial and Applied Mathematics.
[47]
Patrick M. Knupp. 2001. Algebraic mesh quality metrics. SIAM Journal on Scientific Computing 23, 1 (2001), 193?218. DOI: arXiv:https://doi.org/10.1137/S1064827500371499
[48]
Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M. Kaufman. 2020. Incremental potential contact: Intersection- and inversion-free large deformation dynamics. ACM Transactions on Graphics 39, 4 (2020).
[49]
Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M. Kaufman. 2023a. Convergent Incremental Potential Contact. (2023). arxiv:math.NA/2307.15908
[50]
Yifei Li, Tao Du, Kui Wu, Jie Xu, and Wojciech Matusik. 2022. DiffCloth: Differentiable cloth simulation with dry frictional contact. ACM Trans. Graph. (Mar.2022). DOI: Just Accepted.
[51]
Zhehao Li, Qingyu Xu, Xiaohan Ye, Bo Ren, and Ligang Liu. 2023b. DiffFR: Differentiable SPH-based fluid-rigid coupling for rigid body control. ACM Trans. Graph. 42, 6, Article 179 (Dec.2023), 17 pages. DOI:
[52]
Junbang Liang, Ming Lin, and Vladlen Koltun. 2019. Differentiable cloth simulation for inverse problems. Neural Information Processing Systems (2019).
[53]
Micka?l Ly, Romain Casati, Florence Bertails-Descoubes, M?lina Skouras, and Laurence Boissieux. 2018. Inverse elastic shell design with contact and friction. ACM Trans. Graph. 37, 6, Article 201 (Dec.2018), 16 pages. DOI:
[54]
Guirec Maloisel, Espen Knoop, Christian Schumacher, and Moritz Bacher. 2021. Automated routing of muscle fibers for soft robots. IEEE Trans. Robot. 37, 3 (June2021), 996?1008. DOI:
[55]
Charles C. Margossian. 2019. A review of automatic differentiation and its efficient implementation. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 9, 4 (2019), e1305. DOI:
[56]
Aymeric Maury, Gr?goire Allaire, and Fran?ois Jouve. 2017. Shape Optimisation with the Level Set Method for Contact Problems in Linearised Elasticity. (Jan.2017). https://hal.archives-ouvertes.fr/hal-01435325
[57]
Antoine McNamara, Adrien Treuille, Zoran Popovi?, and Jos Stam. 2004. Fluid control using the adjoint method. ACM Transactions on Graphics / SIGGRAPH 2004 23, 3 (Aug.2004).
[58]
Sebastian K. Mitusch, Simon W. Funke, and J?rgen S. Dokken. 2019. dolfin-adjoint 2018.1: Automated adjoints for FEniCS and Firedrake. Journal of Open Source Software 4, 38 (2019), 1292. DOI:
[59]
William S. Moses, Sri Hari Krishna Narayanan, Ludger Paehler, Valentin Churavy, Michel Schanen, Jan H?ckelheim, Johannes Doerfert, and Paul Hovland. 2022. Scalable automatic differentiation of multiple parallel paradigms through compiler augmentation. In Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (SC ?22) . IEEE Press, Article 60, 18 pages.
[60]
Uwe Naumann. 2012. The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation . Vol. 24. SIAM. DOI:
[61]
Miguel Otaduy, Rasmus Tamstorf, Denis Steinemann, and Markus Gross. 2009. Implicit contact handling for deformable objects. Comp. Graph. Forum 28 (042009).
[62]
Julian Panetta, Abtin Rahimian, and Denis Zorin. 2017. Worst-case stress relief for microstructures. ACM Transactions on Graphics 36, 4 (2017). DOI:
[63]
Julian Panetta, Qingnan Zhou, Luigi Malomo, Nico Pietroni, Paolo Cignoni, and Denis Zorin. 2015. Elastic textures for additive fabrication. ACM Trans. Graph. 34, 4, Article 135 (July2015), 12 pages.
[64]
Yi-Ling Qiao, Junbang Liang, Vladlen Koltun, and Ming Lin. 2020. Scalable differentiable physics for learning and control. In International Conference on Machine Learning . PMLR, 7847?7856.
[65]
Michael Rabinovich, Roi Poranne, Daniele Panozzo, and Olga Sorkine-Hornung. 2017. Scalable locally injective mappings. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1.
[66]
Junior Rojas, Eftychios Sifakis, and Ladislav Kavan. 2021. Differentiable implicit soft-body physics. arXiv preprint arXiv:2102.05791 (2021).
[67]
Connor Schenck and Dieter Fox. 2018. SPNets: Differentiable fluid dynamics for deep neural networks. In Proceedings of The 2nd Conference on Robot Learning (Proceedings of Machine Learning Research) , Aude Billard, Anca Dragan, Jan Peters, and Jun Morimoto (Eds.), Vol. 87. PMLR, 317?335. https://proceedings.mlr.press/v87/schenck18a.html
[68]
Teseo Schneider, J?r?mie Dumas, Xifeng Gao, Denis Zorin, and Daniele Panozzo. 2019. PolyFEM. https://polyfem.github.io/ (2019).
[69]
Christian Schumacher, Espen Knoop, and Moritz Bacher. 2020. Simulation-ready characterization of soft robotic materials. IEEE Robot. Autom. Lett. 5, 3 (July2020), 3775?3782. DOI:
[70]
Christian Schumacher, Jonas Zehnder, and Moritz B?cher. 2018. Set-in-stone: Worst-case optimization of structures weak in tension. ACM Trans. Graph. 37, 6, Article 252 (Dec.2018), 13 pages. DOI:
[71]
Sicong Shan, Sung Kang, Jordan Raney, Pai Wang, Lichen Fang, Francisco Candido, Jennifer Lewis, and Katia Bertoldi. 2015. Multistable architected materials for trapping elastic strain energy. Advanced Materials (Deerfield Beach, Fla.) 27 (062015). DOI:
[72]
Ashesh Sharma and Kurt Maute. 2018. Stress-based topology optimization using spatial gradient stabilized XFEM. Structural and Multidisciplinary Optimization 57, 1 (2018), 17?38.
[73]
M?lina Skouras, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, and Markus Gross. 2013. Computational design of actuated deformable characters. ACM Trans. Graph. 32, 4, Article 82 (Jul.2013), 10 pages. DOI:
[74]
David E. Stewart. 2001. Finite-dimensional contact mechanics. Phil. Trans. R. Soc. Lond. A 359 (2001).
[75]
Stanis?aw Stupkiewicz, Jakub Lengiewicz, and Jovze Korelc. 2010. Sensitivity analysis for frictional contact problems in the augmented Lagrangian formulation. Computer Methods in Applied Mechanics and Engineering 199, 33 (July2010), 2165?2176. DOI:
[76]
Javier Tapia, Espen Knoop, Mojmir Mutn?, Miguel A. Otaduy, and Moritz B?cher. 2020. MakeSense: Automated sensor design for proprioceptive soft robots. Soft Rob. 7, 3 (June2020), 332?345. DOI:
[77]
Davi Colli Tozoni, J?r?mie Dumas, Zhongshi Jiang, Julian Panetta, Daniele Panozzo, and Denis Zorin. 2020. A low-parametric rhombic microstructure family for irregular lattices. ACM Trans. Graph. 39, 4, Article 101 (Jul.2020), 20 pages. DOI:
[78]
Davi Colli Tozoni, Yunfan Zhou, and Denis Zorin. 2021. Optimizing contact-based assemblies. ACM Trans. Graph. 40, 6, Article 269 (Dec.2021), 19 pages. DOI:
[79]
F. van Keulen, R. T. Haftka, and N. H. Kim. 2005. Review of options for structural design sensitivity analysis. Part 1: Linear systems. Computer Methods in Applied Mechanics and Engineering 194, 30 (2005), 3213?3243. DOI: Structural and Design Optimization.
[80]
Mickeal Verschoor and Andrei C. Jalba. 2019. Efficient and accurate collision response for elastically deformable models. ACM Trans. on Graph. (TOG) 38, 2 (2019).
[81]
Patrick Wieschollek. 2016. CppOptimizationLibrary. https://github.com/PatWie/CppNumericalSolvers
[82]
Peter Wriggers. 1995. Finite element algorithms for contact problems. Archives of Comp. Meth. in Eng. 2 (121995).
[83]
Jie Xu, Viktor Makoviychuk, Yashraj Narang, Fabio Ramos, Wojciech Matusik, Animesh Garg, and Miles Macklin. 2022. Accelerated Policy Learning with Parallel Differentiable Simulation. (2022). DOI:
[84]
Xiaoting Zhang, Xinyi Le, Zihao Wu, Emily Whiting, and Charlie C. L. Wang. 2016. Data-driven bending elasticity design by shell thickness. Computer Graphics Forum (Proceedings of Symposium on Geometry Processing) 35, 5 (2016), 157?166.
