Rank Reduction AutoEncoders for Mechanical Design: Advancing Novel and Efficient Data-Driven Topology Optimization

Abstract

This work presents a data-driven framework for fast forward and inverse analysis in topology optimization (TO) by combining Rank Reduction Autoencoders (RRAEs) with neural latent-space mappings. The methodology targets the efficient approximation of the relationship between optimized geometries and their corresponding mechanical responses or Quantity of Interest (QoI), with a particular focus on compliance-minimized linear elastic structures. High-dimensional TO results are first compressed using RRAEs, which encode the data into a low-rank approximation via Singular Value Decomposition (SVD), obtained in this sense the most important features that approximate the data. Separate RRAE models are trained for geometry and for different types of QoIs, including scalar metrics, one-dimensional stress fields, and full two-dimensional von Mises stress distributions. The resulting low-dimensional latent coefficients of the latent space 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 benchmark TO problem based on a half MBB beam, using datasets generated via density-based Solid Isotropic Material with Penalization (SIMP) optimization. Numerical results show that the framework enables accurate and computationally efficient surrogate models, with increasing robustness and fidelity as richer QoIs are considered. The methodology also provides a foundation for generative mechanical design by enabling the synthesis of new geometries and responses through latent-space exploration.