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

TL;DR

The paper tackles global search in topology optimization under strong nonlinearity by introducing a data-driven multifidelity design that jointly optimizes material distributions and high-fidelity modeling parameters. It replaces the conventional single-channel VAE with a multi-channel VAE (MC-VAE) and uses an evolutionary framework (NSGA-II) guided by a hypervolume convergence criterion to perform crossover and mutation in a single run. The approach demonstrates improved performance over reference solutions and conventional MFTD in stiffness maximization and maximum-stress minimization by effectively exploring the HF parameter space and enabling/shared learning across channels. This yields more globally optimal lightweight structures with reduced need for extensive parametric HF studies, and sets the stage for extending HF parameter distributions across design domains in future work.

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.

Figures (17)

• Figure 1: Illustration of LF and HF parameter concept.
• Figure 2: Schematic flowchart of the proposed data-driven multifidelity topology design.
• Figure 3: Illustration of the data structure of MC-VAE.
• Figure 4: Generated images comparison between a) the proportional and b) inversely proportional dataset.
• Figure 5: Illustration of the HF modeling.