  We introduce a theory-driven mechanism for learning a neural network model
that performs generative topology design in one shot given a problem setting,
circumventing the conventional iterative process that computational design
tasks usually entail. The proposed mechanism can lead to machines that quickly
response to new design requirements based on its knowledge accumulated through
past experiences of design generation. Achieving such a mechanism through
supervised learning would require an impractically large amount of
problem-solution pairs for training, due to the known limitation of deep neural
networks in knowledge generalization. To this end, we introduce an interaction
between a student (the neural network) and a teacher (the optimality conditions
underlying topology optimization): The student learns from existing data and is
tested on unseen problems. Deviation of the student's solutions from the
optimality conditions is quantified, and used for choosing new data points to
learn from. We call this learning mechanism "theory-driven", as it explicitly
uses domain-specific theories to guide the learning, thus distinguishing itself
from purely data-driven supervised learning. We show through a compliance
minimization problem that the proposed learning mechanism leads to topology
generation with near-optimal structural compliance, much improved from standard
supervised learning under the same computational budget.
