A Regularized Procedure to Generate a Deep Learning Model for Topology Optimization of Electromagnetic Devices

Abstract

The use of behavioral models based on deep learning (DL) to accelerate electromagnetic field computations has recently been proposed to solve complex electromagnetic problems. Such problems usually require time-consuming numerical analysis, while DL allows achieving the topologically optimized design of electromagnetic devices using desktop class computers and reasonable computation times. An unparametrized bitmap representation of the geometries to be optimized, which is a highly desirable feature needed to discover completely new solutions, is perfectly managed by DL models. On the other hand, optimization algorithms do not easily cope with high dimensional input data, particularly because it is difficult to enforce the searched solutions as feasible and make them belong to expected manifolds. In this work, we propose the use of a variational autoencoder as a data regularization/augmentation tool in the context of topology optimization. The optimization was carried out using a gradient descent algorithm, and the DL neural network was used as a surrogate model to accelerate the resolution of single trial cases in the due course of optimization. The variational autoencoder and the surrogate model were simultaneously trained in a multi-model custom training loop that minimizes total loss—which is the combination of the two models’ losses. In this paper, using the TEAM 25 problem (a benchmark problem for the assessment of electromagnetic numerical field analysis) as a test bench, we will provide a comparison between the computational times and design quality for a “classical” approach and the DL-based approach. Preliminary results show that the variational autoencoder manages regularizing the resolution process and transforms a constrained optimization into an unconstrained one, improving both the quality of the final solution and the performance of the resolution process.

Special Issue: Regularization Techniques for Machine Learning and Their Applications

“…The sixth paper is authored by Tucci et al [8] entitled A Regularized Procedure to Generate a Deep Learning Model for Topology Optimization of Electromagnetic Devices. The authors developed a new regularization framework based on a variational autoencoder (VAE) for topology optimization of electromagnetic devices.…”

Curved Domains in Magnetics: A Virtual Element Method Approach for the T.E.A.M. 25 Benchmark Problem

“…Another strategy consists of keeping the mesh fixed and changing the "properties" of the FEM elements [2][3][4][5][6]. In the electromagnetism framework, the "property" can be the presence or absence of the ferromagnetic material.…”

“…In the electromagnetism framework, the "property" can be the presence or absence of the ferromagnetic material. For instance, in [3], the authors apply such a strategy for the T.E.A.M. 25 problem.…”

“…25 problem. They discretise the region with a binary bitmap where the die molds are placed; see Figure 6 of [3]. In particular, black squares (pixel 1) represent a portion of the domain filled with ferromagnetic material, while white squares (pixel 0) represent air.…”

Machine Learning Approaches for Inverse Problems and Optimal Design in Electromagnetism

“…In previous works, authors have proposed several ML models both for solving the direct [9] model and the inverse model [10], focusing attention on optimization through the use of the direct model and highlighting the difficulty behind the inverse models.…”