A multi-point synergistic gradient evolution method for topology optimization leveraging neural network with applications in converged and diverse designs

• Published in: Computational mechanics Vol. 73; no. 1; pp. 105 - 122
• Main Authors: Wang, Chunpeng, Lian, Yanping, Gao, Ruxin, Xiong, Feiyu, Li, Ming-Jian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2024; Springer Nature B.V
• Subjects: Algorithms; Artificial intelligence; Artificial neural networks; Back propagation networks; Business competition; Classical and Continuum Physics; Computational Science and Engineering; Convergence; Design optimization; Design parameters; Engineering; Evolution; Finite element method; Isotropic material; Neural networks; Original Paper; Sensitivity analysis; Theoretical and Applied Mechanics; Topology optimization; Topology optimization; Diverse designs; Loss function; Neural network; Population-based algorithm
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-023-02358-z

Artificial intelligence (AI) methods have been shown to be effective in aiding topology optimization (TO). This paper proposes an artificial neural network (ANN)-based structural TO method, where the advantages of both the traditional gradient-based methods and the population-based approaches are combined to achieve the converged design or design diversity efficiently. In this method, we adopted the ANN as the structural descriptor for a population of structures that broadly samples the design space and the popular gradient-based solution framework (i.e., the solid isotropic material with penalization, SIMP) to integrate the ANN and finite element analysis of the structures. In such a solution framework, the weights and bias associated with the ANN become the design variables to re-parameterize the density fields of a set of designs used in SIMP but independent of the finite element mesh. These design variables are optimized via the ANN’s built-in back-propagation, where a group of points in the design space synergistically evolve under the gradient-based solution framework. Novel loss functions encoding all the sampled structural performances and topology awareness are proposed, including a competitive mechanism-based loss function for converged design and a population diversity-preserving strategy-based loss function to obtain diverse and competitive designs. Correspondingly, a combination of the adjoint method and automatic differentiation algorithm is introduced for the sensitivity analysis. We refer to this method as a multi-point synergistic gradient evolution method. Its efficiency and applicability are demonstrated through 2D and 3D examples. The proposed method is expected to serve as a powerful design tool and further advance the use of AI in TO.