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Computationally Efficient Data-Driven Topology Design Independent from High-Infoentropy Initial Dataset

Jun Yang, Ziliang Wang, Shintaro Yamasaki

TL;DR

An efficient DDTD-based framework capable of being driven from low information-entropy initial datasets is proposed while improving computational efficiency, and a mesh-independent mutation module is introduced as a supplementary source of geometric features, enabling stable exploration under low information-entropy initialization.

Abstract

Topology optimization (TO) has been widely adopted in engineering design; however, it is prone to being trapped in local optima, particularly in strongly nonlinear problems. Sensitivity-free data-driven topology design (DDTD) offers a promising alternative. Nevertheless, existing DDTD-based methods still depend heavily on prior information or sensitivity-based TO methods for initialization, limiting their generality and independence in engineering applications. In this study, an efficient DDTD-based framework capable of being driven from low information-entropy initial datasets is proposed while improving computational efficiency. To reduce the dependence on high information-entropy initial datasets, a mesh-independent mutation module is introduced as a supplementary source of geometric features, enabling stable exploration under low information-entropy initialization. To alleviate the computational bottleneck in DDTD, where all candidate structures require numerical evaluations, a non-AI-based rapid identification algorithm is developed to efficiently identify potential high-performance structures, thereby significantly reducing the number of expensive high-fidelity simulations. The framework generates material distributions on body-fitted meshes to maintain consistency between numerical simulations and physical manufacturing. A signed distance field-based minimum length constraint is further incorporated to ensure reliable mesh generation. Numerical experiments on strongly nonlinear stress-related problems, together with comparisons with sensitivity-based TO methods, demonstrate the effectiveness of the proposed method. In microfluidic reactor and shell design problems involving non-differentiable constraints, the proposed method successfully addresses scenarios that remain challenging for both sensitivity-based TO and conventional DDTD-based methods.

Computationally Efficient Data-Driven Topology Design Independent from High-Infoentropy Initial Dataset

TL;DR

An efficient DDTD-based framework capable of being driven from low information-entropy initial datasets is proposed while improving computational efficiency, and a mesh-independent mutation module is introduced as a supplementary source of geometric features, enabling stable exploration under low information-entropy initialization.

Abstract

Topology optimization (TO) has been widely adopted in engineering design; however, it is prone to being trapped in local optima, particularly in strongly nonlinear problems. Sensitivity-free data-driven topology design (DDTD) offers a promising alternative. Nevertheless, existing DDTD-based methods still depend heavily on prior information or sensitivity-based TO methods for initialization, limiting their generality and independence in engineering applications. In this study, an efficient DDTD-based framework capable of being driven from low information-entropy initial datasets is proposed while improving computational efficiency. To reduce the dependence on high information-entropy initial datasets, a mesh-independent mutation module is introduced as a supplementary source of geometric features, enabling stable exploration under low information-entropy initialization. To alleviate the computational bottleneck in DDTD, where all candidate structures require numerical evaluations, a non-AI-based rapid identification algorithm is developed to efficiently identify potential high-performance structures, thereby significantly reducing the number of expensive high-fidelity simulations. The framework generates material distributions on body-fitted meshes to maintain consistency between numerical simulations and physical manufacturing. A signed distance field-based minimum length constraint is further incorporated to ensure reliable mesh generation. Numerical experiments on strongly nonlinear stress-related problems, together with comparisons with sensitivity-based TO methods, demonstrate the effectiveness of the proposed method. In microfluidic reactor and shell design problems involving non-differentiable constraints, the proposed method successfully addresses scenarios that remain challenging for both sensitivity-based TO and conventional DDTD-based methods.
Paper Structure (16 sections, 18 equations, 18 figures, 1 table)

This paper contains 16 sections, 18 equations, 18 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Representation of material distributions and general formulation
  4. Data processing workflow
  5. Generation and mutation module
  6. Generation module based on deep generative model
  7. Parameter-controlled component-based mutation module
  8. Rapid selection module
  9. Physics-embedded mapping algorithm
  10. Rapid identification algorithm
  11. Minimum length and connectivity constraints
  12. Experiments and discussion
  13. Maximum von Mises stress minimization problem
  14. Microfluidic reactor design problem
  15. Shell structural design problem
  16. ...and 1 more sections

Figures (18)

  • Figure 1: The impact of initial data with different information entropy on conventional DDTD-based methods.
  • Figure 2: Design variables $\rho_i$ and corresponding smoothed material distribution $\phi$.
  • Figure 3: Data processing workflow of the proposed DDTD-based method.
  • Figure 4: Partial shape of parameter-controllable polygon by random parameters.
  • Figure 5: An example of rapid identification algorithm.
  • ...and 13 more figures