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We introduce a theory-driven mechanism for learning a neural network modelthat performs generative topology design in one shot given a problem setting,circumventing the conventional iterative process that computational designtasks usually entail. The proposed mechanism can lead to machines that quicklyresponse to new design requirements based on its knowledge accumulated throughpast experiences of design generation. Achieving such a mechanism throughsupervised learning would require an impractically large amount ofproblem-solution pairs for training, due to the known limitation of deep neuralnetworks in knowledge generalization. To this end, we introduce an interactionbetween a student (the neural network) and a teacher (the optimality conditionsunderlying topology optimization): The student learns from existing data and istested on unseen problems. Deviation of the student's solutions from theoptimality conditions is quantified, and used for choosing new data points tolearn from. We call this learning mechanism "theory-driven", as it explicitlyuses domain-specific theories to guide the learning, thus distinguishing itselffrom purely data-driven supervised learning. We show through a complianceminimization problem that the proposed learning mechanism leads to topologygeneration with near-optimal structural compliance, much improved from standardsupervised learning under the same computational budget.

One-Shot Generation of Near-Optimal Topology through Theory-Driven Machine Learning