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Main Title: Topology Optimisation under Uncertainties with Neural Networks
Author(s): Eigel, Martin
Haase, Marvin
Neumann, Johannes
Type: Article
Abstract: Topology optimisation is a mathematical approach relevant to different engineering problems where the distribution of material in a defined domain is distributed in some optimal way, subject to a predefined cost function representing desired (e.g., mechanical) properties and constraints. The computation of such an optimal distribution depends on the numerical solution of some physical model (in our case linear elasticity) and robustness is achieved by introducing uncertainties into the model data, namely the forces acting on the structure and variations of the material stiffness, rendering the task high-dimensional and computationally expensive. To alleviate this computational burden, we develop two neural network architectures (NN) that are capable of predicting the gradient step of the optimisation procedure. Since state-of-the-art methods use adaptive mesh refinement, the neural networks are designed to use a sufficiently fine reference mesh such that only one training phase of the neural network suffices. As a first architecture, a convolutional neural network is adapted to the task. To include sequential information of the optimisation process, a recurrent neural network is constructed as a second architecture. A common 2D bridge benchmark is used to illustrate the performance of the proposed architectures. It is observed that the NN prediction of the gradient step clearly outperforms the classical optimisation method, in particular since larger iteration steps become viable.
Subject(s): topology optimisation
deep neural networks
model uncertainties
random fields
convolutional neural networks
recurrent neural networks
Issue Date: 12-Jul-2022
Date Available: 5-Aug-2022
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: DFG, 273721697, SPP 1886: Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukturen
Journal Title: Algorithms
Publisher: MDPI
Volume: 15
Issue: 7
Article Number: 241
Publisher DOI: 10.3390/a15070241
EISSN: 1999-4893
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » DeepGreen Deposits

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