A new Neural Network-based methodology for multi-level topology optimisation in structural problems

The optimisation of high-resolution trabecular structures is crucial for various industrial applications due to their resilience to unexpected loads. Current topology optimisation (TO) approaches face challenges like high computational costs and limited topology versatility. Addressing this, a 2-Level Topology Optimization approach was proposed [1], where material is first distributed over the domain (discretised into cells) at the coarse level and then finely redistributed at the fine level into each cell, using TO in both levels. This densitybased multi-level approach ensures the topology versatility of optimised cells while reducing computational costs. Recently, Machine learning (ML) techniques have been considered to enhance the efficiency of TO processes, but current models lack generality in arbitrary domains and boundary conditions. This paper introduces a data-driven surrogate model in the cell-level stage of the 2-Level TO process, leveraging the repetitive shape of cells in coarse discretisation. This ensures methodology versatility across different domains and boundary conditions, mitigating generalisation issues while enhancing the efficiency of the multi-level TO. The methodology details include the TO scheme, U-Net architecture of the surrogate model, creation of the training dataset, and case study evaluations. Numerical analyses compare the proposed approach with traditional Finite Element Method (FEM)-based TO procedures, demonstrating its efficacy in achieving accurate results, optimised topologies, and generalisation capability. The proposed data-driven surrogate model might yield suboptimal structures in some cases. However, this is addressed through a tuning strategy involving a few extra iterations of FEM-based cell TO, without dramatically penalising the achieved speedup.