Robust Topology Optimization Using Multi-Fidelity Variational Autoencoders

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is computationally challenging as it requires repetitive finite element solutions for different candidate designs and different samples of random inputs. To address this challenge, a neural network method is proposed that offers computational efficiency because (1) it builds and explores a low dimensional search space which is parameterized using deterministically optimal designs corresponding to different realizations of random inputs, and (2) the probabilistic performance measure for each design candidate is predicted by a neural network surrogate. This method bypasses the numerous finite element response evaluations that are needed in the standard RTO approaches and with minimal training can produce optimal designs with better performance measures compared to those observed in the training set. Moreover, a multi-fidelity framework is incorporated to the proposed approach to further improve the computational efficiency. Numerical application of the method is shown on the robust design of L-bracket structure with single point load as well as multiple point loads.