Learning hyperparameter predictors for similarity-based multidisciplinary topology optimization

Topology optimization (TO) plays a significant role in industry by providing engineers with optimal material distributions based exclusively on the information about the design space and loading conditions. Such approaches are especially important for current multidisciplinary design tasks in industry, where the conflicting criteria often lead to very unintuitive solutions. Despite the progress in integrating manufacturing constraints into TO, one of the main factors restricting the use of TO in practice is the users’ limited control of the final material distribution. To address this problem, recently, a universal methodology for enforcing similarity to reference structures in various TO methods by applying scaling of elemental energies was proposed. The method, however, requires an expensive hyperparameter sampling, which involves running multiple TO processes to find the design of a given similarity to a reference structure. In this article, we propose a novel end-to-end approach for similarity-based TO, which integrates a machine learning model to predict the hyperparameters of the method, and provide the engineer, at minimal computational cost, with a design satisfying multidisciplinary criteria expressed by the similarity to a reference. The training set for the model is generated based on an academic linear elastic problem, but the model generalizes well to both nonlinear dynamic crash and industrial-scale TO problems. We show the latter by applying the proposed methodology to a real-world multidisciplinary TO problem of a car hood frame, which demonstrates the usefulness of the approach in industrial settings.