Bélières -- Frendo, M Amaury (2023) Learning-based shape optimization PFE - Project Graduation, ENSTA.
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Abstract
During each iteration, conventional shape optimization algorithms require the numerical resolution of several PDEs, including calculating the state, adjoint and step by linear search, for example. These steps are costly and difficult to parallelize. The aim of this work is to propose new algorithms for shape optimization using PINNs. PINNs have the considerable advantage of reducing the number of operations per teration, especially when calculating integrals in dimensions greater than 2, and enable state and adjoint to be computed simultaneously. By focusing on a canonical problem such as the optimization of the optimization for Dirichlet energy, we’ll begin with the mathematical analysis of the Dirichlet energy minimization problem via the the method of fictitious materials, and then implement it. Next, we’ll look at how to implement a geometric optimization algorithm via an intrinsically symplectic neural network.
Item Type: | Thesis (PFE - Project Graduation) |
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Subjects: | Mathematics and Applications |
ID Code: | 9923 |
Deposited By: | amaury Belieres - frendo |
Deposited On: | 24 nov. 2023 15:01 |
Dernière modification: | 24 nov. 2023 15:01 |
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