Differentiable Solver for Time-dependent Deformation Problems with Contact

Zizhou Huang^*1, Davi Colli Tozoni^*1,2, Arvi Gjoka¹, Zachary Ferguson^1,3, Teseo Schneider⁴, Daniele Panozzo¹, Denis Zorin¹

¹New York University · ²nTop · ³Massachusetts Institute of Technology · ⁴University of Victoria · ^*equal contribution

ACM Transactions on Graphics (SIGGRAPH 2024)

Paper Video Code Tutorial ACM DL

Differentiable simulation results across shape, initial condition and material optimization

Abstract

We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed Incremental Potential Contact method for handling contact and friction forces to solve ODE- and PDE-constrained optimization problems on scenes with complex geometry.

It supports static and dynamic problems and differentiation with respect to all physical parameters, including shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation.

We implement our approach on top of the open-source PolyFEM library and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and physical validations.

Keywords

Differentiable simulation, finite element method, elastodynamics, frictional contact.

Results

Shape optimization of a hanger, with stress distribution visualized — **Shape** optimization to minimize stress on a hanger from [Tozoni et al. 2021], with the stress distribution visualized.

Bunny collision before optimization — Initial guess

Bunny collision after optimization — Optimized

Optimize the initial velocity of the yellow bunny to hit the blue bunny into the circle.

Sliding bunny before friction optimization — Initial guess

Sliding bunny after friction optimization — Optimized

Optimize the friction coefficient so the bunny reaches the white line at exactly two seconds.

Open-source code

PolyFEM

The differentiable solver described in this paper is integrated into the open-source PolyFEM finite element library. The data repository holds configuration files that reproduce the examples in the paper.

Documentation GitHub Data

Citation

@article{10.1145/3657648,
  author    = {Huang, Zizhou and Tozoni, Davi Colli and Gjoka, Arvi and Ferguson, Zachary
               and Schneider, Teseo and Panozzo, Daniele and Zorin, Denis},
  title     = {Differentiable solver for time-dependent deformation problems with contact},
  journal   = {ACM Trans. Graph.},
  volume    = {43},
  number    = {3},
  articleno = {31},
  numpages  = {30},
  year      = {2024},
  month     = may,
  publisher = {Association for Computing Machinery},
  address   = {New York, NY, USA},
  issn      = {0730-0301},
  doi       = {10.1145/3657648},
  url       = {https://doi.org/10.1145/3657648}
}