Mathematical density-based topology optimization methods commonly require analytical sensitivity information. In this paper we propose a heuristic approach for topology optimization, targeting the optimization of objective functions for which analytical sensitivities are not available or difficult to obtain. Concretely, sensitivities are substituted by the prediction of a regression model, which is trained based on sampled sensitivity data. This information is obtained from finite differencing, combined with the assumption that local state features, associated with each design variable, are suitable for predicting the corresponding sensitivity. In order to evaluate the proposed method and in order to compare the results to a known optimal baseline solution, it is applied to the problem of optimizing a minimum compliance cantilever. In most experiments, optimized designs similar to the baseline design are obtained, while the number of finite element solver runs is reduced drastically compared to pure finite differencing gradient estimation. As solution quality and the number of required samples depend on the prediction quality, we provide recommendations for the choice of model and features based on the conducted experiments.
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