Differentiable solver for time-dependent deformation problems with contact
CoRR(2022)
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 PDE- and ODE-constrained optimization problems on scenes with a
complex geometry. It support 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
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 in physical
validations.
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