可微函数
计算机科学
解算器
自由度(物理和化学)
自动微分
计算
多边形网格
职位(财务)
算法
编码(集合论)
序列(生物学)
计算科学
数学优化
数学
计算机图形学(图像)
数学分析
经济
集合(抽象数据类型)
物理
程序设计语言
生物
量子力学
遗传学
财务
作者
Tuur Stuyck,Hsiao-yu Chen
出处
期刊:Proceedings of the ACM on computer graphics and interactive techniques
[Association for Computing Machinery]
日期:2023-08-16
卷期号:6 (3): 1-14
被引量:6
摘要
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 cloth and volumetric 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.
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