TO-NODE: Topology optimization with neural ordinary differential equation

Deep learning methods have become attractive recently to accelerate topology optimization (TO) because of their capability to save huge computational costs with negligible sacrifice in the quality of final topologies. However, most current approaches rely on numerical mechanics platforms for training which incur significant computation costs. Further, current approaches are not suited for dynamically changing boundary conditions. This is because these deep learning frameworks once trained using results generated with a specific set of boundary conditions do not readily adapt to others. In this article, we present a novel approach to leverage the abilities of deep learning models for TO. We demonstrate that optimization can be achieved using a neural ordinary differential equation. The evolution of the design variable in each iteration of TO is then achieved by numerical integration of this neural differential equation with respect to the starting design. To improve the quality of the results, two levels of generative adversarial networks are also introduced, at the sequence, and image levels, respectively. The proposed machine learning framework is capable of generating full optimization paths relevant to TO in high resolution within seconds and can address novel unseen boundary conditions.