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.

我们引入了一种通用的可微分求解器，用于解决接触和摩擦的瞬态变形问题。我们的方法使用带有高阶时间积分器的有限元离散化，结合最近提出的增量势接触方法来处理接触力和摩擦力，以解决具有复杂几何形状的场景上的 ODE 和 PDE 约束优化问题。它支持静态和动态问题以及物理问题描述中涉及的所有物理参数的区分，包括形状、材料参数、摩擦参数和初始条件。我们的分析推导的伴随公式是高效的，与正向仿真相比开销较小（对于非线性问题通常小于 10%），并且与正向问题有许多相似之处，允许重用现有正向仿真器代码的大部分。

我们在开源 PolyFEM 库之上实施我们的方法，并通过模拟结果和物理验证证明我们的求解器对形状设计、初始条件优化和材料估计的适用性。