A Prior Reduced Model of Dynamical Systems

  • Haoran Xie
  • Zhiqiang Wang
  • Kazunori Miyata
  • Ye Zhao
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 18)


A reduced model technique for simulating dynamical systems in computer graphics is proposed. Most procedural models of physics-based simulations consist of control parameters in a high-dimensional domain in which the real-time controllability of simulations is an ongoing issue. Therefore, we adopt a separated representation of the model solutions that can be preprocessed offline without relying on the knowledge of the complete solutions. To achieve the functional products in this representation, we utilize an iterative method involving enrichment and projection steps in a tensor formulation. The proposed approaches are successfully applied to different parametric and coupled models.


Model reduction Dynamical system Separated representation  Fixed-point method Tensor product Enrichment step Projection step 



We would like to thank the anonymous reviewers for their valuable comments. This work was supported by JSPS KAKENHI Grant Number 26540051 and JSPS Fellows Grant Number 269549.


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Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Haoran Xie
    • 1
  • Zhiqiang Wang
    • 2
  • Kazunori Miyata
    • 1
  • Ye Zhao
    • 2
  1. 1.School of Knowledge ScienceJapan Advanced Institute of Science and Technology/JSPS Research FellowNomiJapan
  2. 2.Department of Computer ScienceKent State UniversityKentUSA

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