DiffXPBD : Differentiable Position-Based Simulation of Compliant Constraint Dynamics

TL;DR

DiffXPBD introduces an efficient differentiable simulation framework for compliant constrained dynamics, enabling gradient-based optimization of complex geometries, parameters, and external forces with high computational efficiency on CPU and GPU.

Contribution

It provides the first efficient analytical formulation for differentiable XPBD, allowing simultaneous gradient computation for high-resolution simulations with collisions and complex constraints.

Findings

Able to optimize over 26 million DoFs efficiently

Supports automatic differentiation for gradient calculations

Compatible with CPU and GPU hardware

Abstract

We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with respect to a goal function simultaneously leveraging a performant simulation model. The method is efficient, thus enabling differentiable simulations of high resolution geometries and degrees of freedom (DoFs). Collisions are naturally included in the framework. Our differentiable model allows a user to easily add additional optimization variables. Every control variable gradient requires the computation of only a few partial derivatives which can be computed using automatic differentiation code. We demonstrate the efficacy of the method with examples such as elastic material parameter estimation, initial value optimization, optimizing for underlying body shape and pose by only observing the clothing, and optimizing a time-varying external force sequence to match sparse keyframe shapes at specific times. Our approach demonstrates excellent efficiency and we demonstrate this on high resolution meshes with optimizations involving over 26 million degrees of freedom. Making an existing solver differentiable requires only a few modifications and the model is compatible with both modern CPU and GPU multi-core hardware.