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

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.