Image fragmented learning for data-driven topology design

Abstract This paper proposes a data-driven topology design (DDTD) framework, incorporating $$\textit{image\,fragmented\,learning}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>image</mml:mi> <mml:mspace/> <mml:mi>fragmented</mml:mi> <mml:mspace/> <mml:mi>learning</mml:mi> </mml:mrow> </mml:math> that leverages the technique of dividing an image into smaller segments for learning each fragment. This framework is designed to tackle the challenges of high-dimensional, multi-objective optimization problems. Original DDTD methods leverage the sensitivity-free nature and high capacity of deep generative models to effectively address strongly nonlinear problems. However, their training effectiveness significantly diminishes as input size exceeds a certain threshold, which poses challenges in maintaining the high degrees of freedom crucial for accurately representing complex structures. To address this limitation, we split a trained conditional generative adversarial network into two interconnected modules: the first performs dimensionality reduction, compressing high-dimensional data into a lower-dimensional representation, which is then fed into a variational autoencoder (VAE) to generate new low-dimensional data. The second module reconstructs the generated low-dimensional data back into the high-dimensional design space. The effectiveness of the proposed approach is demonstrated through two case studies: the optimization of an L-bracket design problem and a turbulent heat transfer design problem, both involving design variables at a scale unattainable by the conventional VAE-based method.