Data-driven multifidelity topology design with multi-channel variational auto-encoder for concurrent optimization of multiple design variable fields

TL;DR

This paper introduces a gradient-free, data-driven topology optimization framework using a multi-channel variational auto-encoder to efficiently explore multiple design variables simultaneously, avoiding local optima in complex non-linear problems.

Contribution

It proposes a novel multi-channel VAE architecture for concurrent optimization of multiple design variables, enabling comprehensive single-run optimization without extensive parametric studies.

Findings

Successfully optimized a maximum stress minimization problem with strong non-linearity.

Demonstrated improved global search capability over traditional methods.

Validated the framework's effectiveness in complex, non-linear topology design tasks.

Abstract

The objective of this study is to establish a gradient-free topology optimization framework that facilitates more global solution searches to avoid entrapping in undesirable local optima, especially in problems with strong non-linearity. The framework utilizes a data-driven multifidelity topology design, where solution candidates resulting from low-fidelity optimization problems are iteratively updated by a variational auto-encoder (VAE) and high-fidelity (HF) evaluation. A key step in the solution update involves constructing HF models by extruding VAE-generated material distributions to a constant thickness (the HF modeling parameter) across all candidates, which limits exploration of the parameter space and requires extensive parametric studies outside the optimization loop. To achieve comprehensive optimization in a single run, we propose a multi-channel image data architecture that stores material distributions and HF modeling parameters in separate channels, allowing simultaneous optimization of the HF parameter space. We demonstrated the efficacy of the proposed framework by solving a maximum stress minimization problem, characterized by strong non-linearity due to its minimax formulation.