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

TL;DR

This paper presents a theory-driven machine learning approach for one-shot topology generation that leverages optimality conditions to produce near-optimal designs efficiently, avoiding extensive data requirements.

Contribution

It introduces a novel interaction-based learning mechanism that combines domain theory with neural networks for rapid, near-optimal topology design without extensive supervised data.

Findings

Achieves near-optimal structural compliance in topology design.

Outperforms standard supervised learning methods.

Reduces computational cost for topology optimization.

Abstract

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.