Stochastic Gradient Recycling for Efficient Topology Optimization Under Uncertainty
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We consider structural and topology optimization problems with probabilistic parameters and propose a class of stochastic optimization methods aimed at drastically reducing computational cost. The key idea is to limit evaluations of the expensive state equation by using stochastic, sample-based integration strategies in which gradient information from previous iterations is adaptively recombined. This results in an increasingly accurate gradient estimator that can be used within standard optimization frameworks. The proposed approaches bridge deterministic and fully stochastic methods, retaining convergence guarantees while achieving substantial computational savings. The methods are demonstrated on a range of topology optimization problems under uncertainty and chance-constrained problems, including examples from elasticity, acoustics and optics. In all cases, the approaches achieve solutions of comparable quality to traditional methods at a fraction of the computational cost.
