Deep deterministic policy gradient and graph attention network for geometry optimization of latticed shells

Abstract

This paper proposes a combined approach of deep deterministic policy gradient (DDPG) and graph attention network (GAT) to the geometry optimization of latticed shells with surface shapes defined by a Bézier control net. The optimization problem is formulated to minimize the strain energy of the latticed structures with heights of the Bézier control points as design variables. The information of the latticed shells, including nodal configurations, element properties and internal forces, and the Bézier control net, consisting of control points and control net, are represented as graphs using node feature matrices, adjacency matrices, and weighted adjacency matrices. A specifically designed DDPG agent utilizes GAT and matrix manipulations to observe the state of the structure through the graphs, and decides which and how Bézier control points to move. The agent is trained to excel in the task through a reward signal computed from changes in the strain energy in each optimization step. As shown in numerical examples, the trained agent can effectively optimize structures of different sizes, control nets, configurations, and initial geometries from those used during the training. The performance of the trained agent is competitive compared to particle swarm optimization and simulated annealing despite using a lower computational cost.