Adaptive Topological Optimization via Graph Neural Networks

Abstract

This paper introduces a novel optimization framework based on graph neural networks (GNNs) designed for geometric transformation optimization. Traditional optimization methods often rely on handcrafted objective functions and are limited in their ability to handle complex geometric transformations. This work leverages the power of GNNs to learn a mapping of geometric transformations, enabling automated optimization. We propose a method that utilizes a graph representation of the transformation space, where nodes represent geometric elements and edges represent the transformations applied to them. A GNN is trained to predict the optimal transformation sequence, allowing for efficient and robust optimization of complex geometric patterns. The core mechanism focuses on learning a robust representation of the transformation space through graph neural networks, facilitating the discovery of optimal geometric transformations. The paper demonstrates the effectiveness of this approach through comprehensive experiments on several challenging geometric transformation scenarios, highlighting its superior performance compared to traditional optimization techniques. The results underscore the potential of GNNs for automating geometric transformation optimization, particularly in scenarios involving intricate patterns and high-dimensional transformations.