Rank reduction autoencoders for mechanical design: Learning structured latent manifolds for topology optimization

This work presents a data-driven framework for fast forward and inverse analyses in topology optimization by combining Rank Reduction Autoencoders with neural latent-space mappings. The methodology targets the efficient approximation of the relationship between optimized geometries and their corresponding mechanical responses or quantities of interest with a particular focus on compliance-minimized linear elastic structures. High-dimensional topology optimization results are first compressed using Rank Reduction Autoencoders, which encode the data into low-dimensional manifolds via Singular Value Decomposition, thus extracting the most important (latent) features. Separate Rank Reduction Autoencoder models are trained for geometry and for different types of quantities of interest, including scalar metrics, one-dimensional stress fields, and full two-dimensional von Mises stress distributions. The resulting low-dimensional latent manifolds are then related through multilayer perceptrons to address both direct problems – predicting structural responses from geometry – and inverse problems—recovering geometries from prescribed performance targets. The proposed approach is demonstrated on a half MBB beam and a cantilever beam, with the latter studied under separate and simultaneous variations in volume fraction and load position, using datasets generated via density-based Solid Isotropic Material with Penalization optimization. Numerical results show that the framework enables accurate and computationally efficient surrogate models, with increasing robustness and fidelity as richer quantities of interest are considered. The methodology also shows potential for generative mechanical design through preliminary examples of new geometries and response synthesis via latent-space exploration.