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Data-driven multifidelity and multiscale topology optimization based on phasor-based evolutionary de-homogenization

Shuzhi Xu, Yifan Guo, Hiroki Kawabe, Kentaro Yaji

TL;DR

This work tackles the computational burden and manufacturability challenges of multiscale topology optimization by introducing an evolutionary de-homogenization framework that couples MultiFidelity Topology Design with phasor-based de-homogenization. By compressing low-fidelity design variables with PCA, decoding them through a phasor-based mapping to high-fidelity geometries, and optimizing in a latent space via NSGA-II and VAE-enabled crossover (with mutation realized through image-based deformation), the approach achieves efficient, gradient-free design exploration. Numerical studies on double-clamp and L-bracket beams, as well as multi-load scenarios, demonstrate improved stiffness, buckling resistance, and stress distribution, with favorable trade-offs and robustness compared with SIMP and rank-2 lattice baselines. The framework shows practical potential for fast, fabrication-aware multiscale designs, while highlighting avenues for extending to 3D, experimental validation, and further generative-model enhancements.

Abstract

Multiscale topology optimization is crucial for designing porous infill structures with high stiffness-to-weight ratios and excellent energy absorption. Although gradient-based methods provide a rigorous framework, they are computationally expensive and struggle to capture cross-scale sensitivities in nonlinear settings. Moreover, the resulting hierarchical geometries are often overly complex and lack macroscopically meaningful features. To overcome these issues, we propose an evolutionary de-homogenization framework that couples MultiFidelity Topology Design (MFTD) with a phasor-based de-homogenization technique. The framework translates low-dimensional geometric descriptors into manufacturable high-resolution structures through a hybrid evolutionary algorithm integrating NSGA-II selection, VAE-enabled latent space crossover, and a novel image deformation-based mutation operator. This gradient-free approach achieves efficient optimization while ensuring geometric continuity. Numerical results confirm that the method effectively balances efficiency and design flexibility, offering a scalable pathway for fabrication-aware multiscale structural optimization.

Data-driven multifidelity and multiscale topology optimization based on phasor-based evolutionary de-homogenization

TL;DR

This work tackles the computational burden and manufacturability challenges of multiscale topology optimization by introducing an evolutionary de-homogenization framework that couples MultiFidelity Topology Design with phasor-based de-homogenization. By compressing low-fidelity design variables with PCA, decoding them through a phasor-based mapping to high-fidelity geometries, and optimizing in a latent space via NSGA-II and VAE-enabled crossover (with mutation realized through image-based deformation), the approach achieves efficient, gradient-free design exploration. Numerical studies on double-clamp and L-bracket beams, as well as multi-load scenarios, demonstrate improved stiffness, buckling resistance, and stress distribution, with favorable trade-offs and robustness compared with SIMP and rank-2 lattice baselines. The framework shows practical potential for fast, fabrication-aware multiscale designs, while highlighting avenues for extending to 3D, experimental validation, and further generative-model enhancements.

Abstract

Multiscale topology optimization is crucial for designing porous infill structures with high stiffness-to-weight ratios and excellent energy absorption. Although gradient-based methods provide a rigorous framework, they are computationally expensive and struggle to capture cross-scale sensitivities in nonlinear settings. Moreover, the resulting hierarchical geometries are often overly complex and lack macroscopically meaningful features. To overcome these issues, we propose an evolutionary de-homogenization framework that couples MultiFidelity Topology Design (MFTD) with a phasor-based de-homogenization technique. The framework translates low-dimensional geometric descriptors into manufacturable high-resolution structures through a hybrid evolutionary algorithm integrating NSGA-II selection, VAE-enabled latent space crossover, and a novel image deformation-based mutation operator. This gradient-free approach achieves efficient optimization while ensuring geometric continuity. Numerical results confirm that the method effectively balances efficiency and design flexibility, offering a scalable pathway for fabrication-aware multiscale structural optimization.

Paper Structure

This paper contains 28 sections, 37 equations, 15 figures.

Table of Contents

  1. Introduction
  2. Multifidelity model formulation
  3. Overview of multifidelity model
  4. Geometry mapping
  5. Detail pixal-based structure from phasor-based de-homogenization
  6. Explicit geometry extraction and postprocessing
  7. Optimization model and its numerical implementation
  8. Optimization formulation with latent space evolution
  9. Initial design generation
  10. Selection
  11. Crossover
  12. Mutation: deformation-based mutation via radial sampling perturbation
  13. Numerical examples
  14. Double clamper beam design
  15. Preparation of initial design
  16. ...and 13 more sections

Figures (15)

  • Figure 1: The whole procesure for the multifidelity modelling, in which a double clamped beam is taken as an example.
  • Figure 2: The illustration of the considered microstructures: (a) the orthotropic properties of composite material and its corresponding geometry configuration; (b) the corresponding interpolation figures.
  • Figure 3: The overview of the multifidelity modeling process.
  • Figure 4: The mapping process for the phasor-based de-homogenization.
  • Figure 5: Schematic illustration of geometry extraction and postprocessing.
  • ...and 10 more figures