Non-Convexity in Topology Optimization: Analysis Using Deep Learning

Hertlein, Nathan (Air Force Research Laboratory)

Andrew Gillman
Philip R. Buskohl

Computational Structure Mechanics

Topology optimization (TO) has become a popular tool within DoD and the private sector for designing optimal structures. Advances in additive manufacturing have accelerated this trend. Many recent technical contributions to the field of TO have involved the introduction of filters that promote manufacturability of optimal designs, but these filters—along with widely-used material penalization schemes—have long been known to introduce non-convexity into even the simplest objective functions used in TO. Because TO relies on gradient-based optimizers, this creates the risk of local optimality. We develop a better understanding of the frequency of and practical effects of TO getting stuck in local optima. To date, both theoretical and numerical studies into these effects have been hindered by the extremely large design space associated with TO. Therefore, we use high-performance computing (HPC) to train and test a series of deep learning surrogate models which have been shown to achieve better optima than TO in some cases. We then use these ‘over-performers' as a window into the practical effects of non-convexity for a series of TO parameter sets. By relying on parallelization to execute hundreds of simulations simultaneously and GPU-computing to facilitate deep learning, the approach developed here could be leveraged to benchmark new TO filtering and penalization schemes in future work.