ReLU neural networks have been modelled as constraints in mixed integer linear programming (MILP), enabling surrogate-based optimisation in various domains and efficient solution of machine learning certification problems. However, previous works are mostly limited to MLPs. Graph neural networks (GNNs) can learn from non-euclidean data structures such as molecular structures efficiently and are thus highly relevant to computer-aided molecular design (CAMD). We propose a bilinear formulation for ReLU Graph Convolutional Neural Networks and a MILP formulation for ReLU GraphSAGE models. These formulations enable solving optimisation problems with trained GNNs embedded to global optimality. We apply our optimization approach to an illustrative CAMD case study where the formulations of the trained GNNs are used to design molecules with optimal boiling points.

翻译：ReLU神经网络已被建模为混合整数线性规划（MILP）中的约束条件，从而能够实现跨领域基于替代模型的优化以及机器学习认证问题的高效求解。然而，先前的研究大多局限于多层感知机。图神经网络（GNN）能够高效地从分子结构等非欧几里得数据结构中学习，因此与计算机辅助分子设计（CAMD）高度相关。我们针对ReLU图卷积神经网络提出了一种双线性公式，并为ReLU GraphSAGE模型建立了MILP公式。这些公式使得嵌入训练后GNN的优化问题能够以全局最优方式求解。我们将该优化方法应用于一个说明性CAMD案例研究，其中利用训练后GNN的公式设计具有最优沸点的分子。