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    Accurately Solving Physical Systems with Graph Learning

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    Type
    Preprint
    Authors
    Shao, Han cc
    Kugelstadt, Tassilo
    Pałubicki, Wojciech
    Bender, Jan
    Pirk, Sören
    Michels, Dominik L.
    KAUST Department
    Applied Mathematics & Computational Sci
    Applied Mathematics and Computational Science Program
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Date
    2020-06-06
    Permanent link to this record
    http://hdl.handle.net/10754/663900
    
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    Abstract
    Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods. A video showing dynamic results of our graph learning assisted simulations of elastic rods can be found on the project website available at http://computationalsciences.org/publications/shao-2020-physical-systems-graph-learning.html .
    Publisher
    arXiv
    arXiv
    2006.03897
    Additional Links
    https://arxiv.org/pdf/2006.03897
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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