Multiscale topology optimization via dual neural networks and cutting level sets with non-uniform parameterized microstructures

This paper introduces MTO-DNNCLS, a novel multiscale topology optimization (TMO) framework using dual neural networks and cutting level sets. It designs graded lattice structures with non-uniform microstructures, implicitly represented by level set functions combined from multiple prototypes. Non-uniformity is achieved by adjusting cutting height variables. Additionally, two neural networks are employed: one for neural reparameterization and another as a surrogate model. Specifically, the first neural network (NN) takes predefined point coordinates as input, outputting cutting height variables that determine the microstructure. Through neural reparameterization, the multiscale structure evolves iteratively based on the response analysis results and loss functions. Meanwhile, another neural network is utilized to construct a high-precision surrogate model between the cutting height variables to the elasticity tensor and volume fraction, reducing computational costs of real-time homogenization. The reparameterization process embedded with the surrogate model enables direct internal gradient propagation, eliminating the need for manual sensitivity derivation and significantly simplifying sensitivity analysis. Compliance minimization and shape matching examples are presented to demonstrate the effectiveness and robustness of the proposed framework. Finally, additive manufacturing (AM) and mechanical testing are employed to validate that the obtained non-uniform microstructure exhibits superior stiffness and strength compared to the uniform microstructure.