Real-time topology optimization via learnable mappings

TL;DR

The paper addresses the high computational cost of topology optimization by proposing a real-time, data-driven framework that predicts optimal topologies and stress fields without iterative solvers. It combines a latent-space autoencoder with a fully-connected network that maps problem parameters to the latent representation, enabling fast decoding to the topology via a learned decoder. Training data are generated from SIMP-based TO, including Von Mises and dominant principal stress fields, and the approach is demonstrated on a 2D MBB beam and a 3D bridge, achieving substantial speed-ups (up to ~287×) with high accuracy (BAs around 98–99% for topologies and low MAE/RMSE for stress fields). This method offers real-time capability for conceptual design and rapid design exploration, while acknowledging the need for representative training data and potential consistency risks inherent to purely data-driven predictions.

Abstract

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering contexts. This work proposes a multi-stage machine learning strategy that aims to predict an optimal topology and the related stress fields of interest, either in 2D or 3D, without resorting to any iterative analysis and design process. The overall topology optimization is treated as regression task in a low-dimensional latent space, that encodes the variability of the target designs. First, a fully-connected model is employed to surrogate the functional link between the parametric input space characterizing the design problem and the latent space representation of the corresponding optimal topology. The decoder branch of an autoencoder is then exploited to reconstruct the desired optimal topology from its latent representation. The deep learning models are trained on a dataset generated through a standard method of topology optimization implementing the solid isotropic material with penalization, for varying boundary and loading conditions. The underlying hypothesis behind the proposed strategy is that optimal topologies share enough common patterns to be compressed into small latent space representations without significant information loss. Results relevant to a 2D Messerschmitt-Bölkow-Blohm beam and a 3D bridge case demonstrate the capabilities of the proposed framework to provide accurate optimal topology predictions in a fraction of a second.

Figures (12)

• Figure 1: Scheme of the proposed deep learning pipeline.
• Figure 2: MBB beam. Half-beam with details of an exemplary loading condition and allowed locations of the force vector application point.
• Figure 3: MBB beam. Exemplary comparisons of optimal topologies obtained using the SIMP-based procedure and through the proposed framework. Results in each box are obtained for varying locations and orientations of the acting force. For each case, the accuracy of the predicted topology is measured in terms of binary accuracy (BA), mean absolute error (MAE) and root mean squared error (RMSE).
• Figure 4: MBB beam. Scheme of the combined stress fields computation as an element-wise multiplication between (a) the optimal topology and the corresponding VM stress field, (b) the optimal topology and the corresponding TC stress field.
• Figure 5: MBB beam. Exemplary comparisons of optimal topologies, VM and TC stress fields, and the corresponding combined fields, obtained using the SIMP-based procedure and through the proposed framework. Results in each box are obtained for varying locations and orientations of the acting force. For each case, the accuracy of the predictions is measured in terms of binary accuracy, mean absolute error and root mean squared error.