Differentiable solver for time-dependent deformation problems with contact

TL;DR

This paper presents a differentiable finite element solver for time-dependent deformation with contact and friction, enabling efficient optimization of physical parameters in complex scenes.

Contribution

A novel differentiable solver that integrates contact handling with high-order time integration for deformation problems, supporting parameter optimization.

Findings

Efficient adjoint formulation with less than 10% overhead.

Successful application to shape design and material estimation.

Open-source implementation with physical validation.

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 involved in the physical problem description, which include 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, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code. 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.