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

ACM Transactions on Graphics (presented at SIGGGRAPH 2024)

Paper (12.3MB) Code Tutorial Video

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.

Open Source Code

PolyFEM

Open-source finite element library.

Data

Configuration files to reproduce examples on the paper.

Results

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

Initial Guess

Optimized

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

Initial Guess

Optimized

Optimize friction coefficient so that the bunny reach the white line at exactly 2 seconds.

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},
 
                        year = {2024},
 
                        issue_date = {June 2024},
 
                        publisher = {Association for Computing Machinery},
 
                        address = {New York, NY, USA},
 
                        volume = {43},
 
                        number = {3},
 
                        issn = {0730-0301},
 
                        url = {https://doi.org/10.1145/3657648},
 
                        doi = {10.1145/3657648},
 
                        journal = {ACM Trans. Graph.},
 
                        month = {may},
 
                        articleno = {31},
 
                        numpages = {30},
 
                        keywords = {Differentiable simulation, finite element method, elastodynamics, frictional contact}

                        }

Related Works

Soft Pneumatic Actuator Design using Differentiable Simulation
Arvi Gjoka, Espen Knoop, Moritz Bacher, Denis Zorin, Daniele Panozzo
SIGGRAPH, 2024

Cut-Cell Microstructures for Two-scale Structural Optimization
Davi Colli Tozoni, Zizhou Huang, Daniele Panozzo, Denis Zorin
SGP, 2024

Incremental Potential Contact: Intersection- and Inversion-free Large Deformation Dynamics
Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, Danny M. Kaufman
ACM Transactions on Graphics (SIGGRAPH), 2020