Equivariant deep learning for 3D topology optimization

Abstract

The 21st century witnessed the ascent of deep learning, paving the way for data-driven topology optimization approaches via neural networks. This paradigm shift holds the promise of significant speed-ups compared to classical methods; however, deep learning still faces challenges related to generalization and the requirement for training data. Moreover, the field suffers from a dramatic lack of research infrastructure, which hampers both progress and comparability of results. Notably, prior to our research, neither a reliable yet flexible code base nor public three-dimensional datasets existed. We tackled these challenges by contributing a new public dataset and developing a Python library for three-dimensional topology optimization utilizing deep learning. Additionally, we demonstrate that incorporating physical information into the training process significantly reduces the reliance on extensive training data and enhances overall generalization capabilities.

This work consists of four publications. The initial publication introduces the SELTO dataset, comprising nearly 10,000 three-dimensional samples, each providing topology optimization problems and corresponding solutions. The second publication presents DL4TO, a pioneering PyTorch-based deep learning library for topology optimization, accompanied by comprehensive documentation and online tutorials. The third publication showcases the efficacy of equivariant neural networks and a physics-inspired data preprocessing strategy, substantially reducing the need for extensive training datasets and enhancing generalization capabilities. Finally, the fourth paper employs neural operators to replace the PDE solver in the widely used SIMP method, which is its primary bottleneck. This publication underscores the efficacy of equivariance in learned methods and emphasizes the crucial role of a gradient-consistent loss function when applied in a gradient-based optimization scheme like SIMP.