We present a novel, fast differentiable simulator for soft-body learning and
control applications. Existing differentiable soft-body simulators can be
classified into two categories based on their time integration methods:
Simulators using explicit time-stepping schemes require tiny time steps to
avoid numerical instabilities in gradient computation, and simulators using
implicit time integration typically compute gradients by employing the adjoint
method and solving the expensive linearized dynamics. Inspired by Projective
Dynamics (PD), we present Differentiable Projective Dynamics (DiffPD), an
efficient differentiable soft-body simulator based on PD with implicit time
integration. The key idea in DiffPD is to speed up backpropagation by
exploiting the prefactorized Cholesky decomposition in forward PD simulation.
In terms of contact handling, DiffPD supports two types of contacts: a
penalty-based model describing contact and friction forces and a
complementarity-based model enforcing non-penetration conditions and static
friction. We evaluate the performance of DiffPD and observe it is 4-19 times
faster compared with the standard Newton's method in various applications
including system identification, inverse design problems, trajectory
optimization, and closed-loop control. We also apply DiffPD in a
reality-to-simulation (real-to-sim) example with contact and collisions and
show its capability of reconstructing a digital twin of real-world scenes.

本文介绍了一种新型、快速可微的软体学习和控制应用模拟器 - Differentiable Projective Dynamics (DiffPD)，它以 Projective Dynamics (PD) 为基础具有隐式时间积分；DiffPD 利用向前 PD 模拟中的预因式化 Cholesky 分解加速反向传播，并在接触处理方面支持惩罚式模型和补偿式模型两种类型的接触。DiffPD 的表现非常优秀，可用于实现时域系统识别、逆向设计、轨迹优化和闭环控制应用。此外，利用 DiffPD 进行真实环境到仿真环境（real-to-sim）的数字化建模等方面的研究也取得了良好的成果。