Deep Learning-Based Accuracy Upgrade of Reduced Order Models in Topology Optimization

Abstract

Topology optimization problems pose substantial requirements in computing resources, which become prohibitive in cases of large-scale design domains discretized with fine finite element meshes. A Deep Learning-assisted Topology OPtimization (DLTOP) methodology was previously developed by the authors, which employs deep learning techniques to predict the optimized system configuration, thus substantially reducing the required computational effort of the optimization algorithm and overcoming potential bottlenecks. Building upon DLTOP, this study presents a novel Deep Learning-based Model Upgrading (DLMU) scheme. The scheme utilizes reduced order (surrogate) modeling techniques, which downscale complex models while preserving their original behavioral characteristics, thereby reducing the computational demand with limited impact on accuracy. The novelty of DLMU lies in the employment of deep learning for extrapolating the results of optimized reduced order models to an optimized fully refined model of the design domain, thus achieving a remarkable reduction of the computational demand in comparison with DLTOP and other existing techniques. The effectiveness, accuracy and versatility of the novel DLMU scheme are demonstrated via its application to a series of benchmark topology optimization problems from the literature.

Index Matrices—Based Software Implementation of Power Electronic Circuit Design

“…The paper presents an integrated approach to the modeling and design of power electronic devices, based on an index matrix tool. Compared to other applied methods for studying the behavior of electronic converters [19][20][21][22][23][24][25], the proposals are characterized by versatility, reduced requirements for computational resources, robustness of the solution, and a high potential for algorithmization. Thus, it is highly suitable for the purposes of training in power electronics, as well as in research and engineering practice.…”

“…Although basic properties of IMs have been studied in [10,11], a full review on their application is unpublished. Their usage in modeling of electrical circuits is very rare (an example is given in [18]), and their implementation requires additional training and the development of process automation software [19][20][21][22][23][24][25].…”

“…Static methods Sum() and Multiplication() implement the operations, which are considered in (7) and (11). The method Solve() transforms a R-IM analog of discrete dynamical system model (21) (see ( 48)) to a R-IM analog of equation (20) in order that state variables can be calculated in a step-wise manner at each simulation step. In this process, the auxiliary method Parts() is used in distinguishing current values from previous ones.…”

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“…Finally, let us consider the project ADDOPTML "ADDitively Manufactured OPTimized Structures by means of Machine Learning" also belonging to the Marie Skłodowska-Curie Actions (MSCA) Research and Innovation Staff Exchange (RISE) H2020-MSCA-RISE-2020. Kallioras, Nordas, and Lagaros (2021) describe the deep learning based topology optimization developed in the project coordinated by Greek ETHNICON METSOVION POLYTECHNION and implemented in the consortium of as many as 12 other beneficiaries (6 from Academia, 6 from Industry) and a partner organization, a university from Jordan.…”