Scalable Stress-Constrained Topology Optimization: A Simultaneous Approach Based on Machine Learning

Abstract

Large-scale topology optimization (TO) remains computationally demanding, especially for stress-constrained problems. To address this challenge, we propose the simultaneous neural topology optimization (SNTO) framework where state, adjoint, and design variables are represented with custom neural networks (NNs) whose parameters are jointly optimized within a single loop using adjoint analysis and automatic differentiation. The loss function combines the design objective, an aggregation of the local stress constraints, and the potential energy functionals. Our NNs have a unique architecture that accelerates convergence while capturing the sharp gradients and boundaries which are critical to stress-constrained TO. To scale to millions of degrees of freedom, we develop a hardware-aware training scheme in which the design domain is partitioned into subdomains distributed across multiple graphics processing units (GPUs). To control peak GPU memory, we further slice each subdomain into smaller regions whose loss gradients are evaluated sequentially and accumulated. Unlike domain decomposition, our partitioning naturally ensures field continuity across subdomains without additional loss terms. We first evaluate SNTO on two-dimensional (2D) stress-constrained benchmarks and compare the results to a conventional finite element-based approach, showing that SNTO produces designs with sharper boundaries and smaller gray areas. We then solve three-dimensional (3D) problems with up to eight million collocation points on eight GPUs. The training time decreases nearly in proportion to the number of GPUs and the peak GPU memory is reduced by increasing the number of sub-slices. Overall, SNTO offers an effective pathway to large-scale stress-constrained TO on limited computational resources.

arXiv comment41 pages, 19 figures, journal paper