Multiscale topology optimization using machine learning and displacement-driven microstructures

Multiscale topology optimization (MSTO) enables the design of hierarchical structures with enhanced performance and complexity. However, solving nested optimization problems at multiple scales imposes high computational costs. This paper introduces a machine learning-based MSTO (ML-MSTO) framework that leverages displacement-driven topology-optimized microstructures (TOMs). An artificial neural network is trained to predict homogenized stiffness tensors of TOMs based on macroscale densities and nodal displacements. This surrogate model enables efficient macroscale outer-loop optimization by avoiding microscale inner-loop optimization. Sensitivities are computed analytically from the neural network’s Jacobian, eliminating the need for finite differences. The method is demonstrated on 2D and 3D benchmark problems, generating high-fidelity, non-periodic multiscale structures with excellent compliance performance.