Reference : A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs |

E-prints/Working papers : Already available on another site | |||

Engineering, computing & technology : Civil engineering Engineering, computing & technology : Computer science Engineering, computing & technology : Mechanical engineering Engineering, computing & technology : Multidisciplinary, general & others | |||

Computational Sciences; Physics and Materials Science | |||

http://hdl.handle.net/10993/45257 | |||

A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs | |

English | |

Dehghani, Hamidreza [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >] | |

Zilian, Andreas [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >] | |

Dec-2020 | |

29 | |

No | |

[en] Hybrid training algorithm ; Modified Genetic Algorithm ; Multilevel Stochastic Gradient Descent ; Artificial Neural Network ; Data-driven computational mechanics ; Physics Informed ANN | |

[en] We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy
and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs via ANNs (Artificial Neural Networks). This presented approach allows the selection of a number of locations of interest at which the state variables are expected to fulfil the governing equations associated with a physical problem. Unlike classical PDE approximation methods such as finite differences or the finite element method, there is no need to establish and reconstruct the physical field quantity throughout the computational domain in order to predict the mechanical response at specific locations of interest. The basic idea of MGA-MSGD is the manipulation of the learnable parametersâ€™ components responsible for the error explosion so that we can train the network with relatively larger learning rates which avoids trapping in local minima. The proposed training approach is less sensitive to the learning rate value, training points density and distribution, and the random initial parameters. The distance function to minimise is where we introduce the PDEs including any physical laws and conditions (so-called, Physics Informed ANN). The Genetic algorithm is modified to be suitable for this type of ANN in which a Coarse-level Stochastic Gradient Descent (CSGD) is exploited to make the decision of the offspring qualification. Employing the presented approach, a considerable improvement in both accuracy and efficiency, compared with standard training algorithms such classical SGD and Adam optimiser, is observed. The local displacement accuracy is studied and ensured by introducing the results of Finite Element Method (FEM) at sufficiently fine mesh as the reference displacements. A slightly more complex problem is solved ensuring the feasibility of the methodology | |

University of Luxembourg: Institute of Computational Engineering and Sciences | |

Fonds National de la Recherche - FnR (PRIDE17/12252781) ; Luxembourg Ministry of Economy (FEDER 2018-04-024) | |

Researchers ; Professionals ; Students | |

http://hdl.handle.net/10993/45257 | |

https://arxiv.org/pdf/2012.11517.pdf |

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