Anderson Acceleration for Geometry Optimization and Physics Simulation

Yue Peng University of Science and Technology of China Bailin Deng Cardiff University Juyong Zhang University of Science and Technology of China Fanyu Geng University of Science and Technology of China Wenjie Qin University of Science and Technology of China Ligang Liu University of Science and Technology of China

Geometric Modeling and Processing mathscidoc:2012.16001

ACM Transactions on Graphics (SIGGRAPH), 37, (4), 42, 2018.8
Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for interactive applications. Local-global solvers developed in recent years can quickly compute an approximate solution to such problems, making them an attractive choice for applications that prioritize efficiency over accuracy. However, these solvers suffer from lower convergence rate, and may take a long time to compute an accurate result. In this paper, we propose a simple and effective technique to accelerate the convergence of such solvers. By treating each local-global step as a fixed-point iteration, we apply Anderson acceleration, a well-established technique for fixed-point solvers, to speed up the convergence of a local-global solver. To address the stability issue of classical Anderson acceleration, we propose a simple strategy to guarantee the decrease of target energy and ensure its global onvergence. In addition, we analyze the connection between Anderson acceleration and quasi-Newton methods, and show that the canonical choice of its mixing parameter is suitable for accelerating local-global solvers. Moreover, our technique is effective beyond classical local-global solvers, and can be applied to iterative methods with a common structure. We evaluate the performance of our technique on a variety of geometry optimization and physics simulation problems. Our approach significantly reduces the number of iterations required to compute an accurate result, with only a slight increase of computational cost per iteration. Its simplicity and effectiveness makes it a promising tool for accelerating existing algorithms as well as designing efficient new algorithms.
Fixed-point iterations, numerical optimization, parallel computing, projective dynamics, geometry processing
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@inproceedings{yue2018anderson,
  title={Anderson Acceleration for Geometry Optimization and Physics Simulation},
  author={Yue Peng, Bailin Deng, Juyong Zhang, Fanyu Geng, Wenjie Qin, and Ligang Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201227154215823484728},
  booktitle={ACM Transactions on Graphics (SIGGRAPH)},
  volume={37},
  number={4},
  pages={42},
  year={2018},
}
Yue Peng, Bailin Deng, Juyong Zhang, Fanyu Geng, Wenjie Qin, and Ligang Liu. Anderson Acceleration for Geometry Optimization and Physics Simulation. 2018. Vol. 37. In ACM Transactions on Graphics (SIGGRAPH). pp.42. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201227154215823484728.
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