A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to estimate an optimal control. A key piece in the present architecture is our boundary injected message passing neural network. This will produce more accurate predictions that are considerably more stable in proximity of the boundary. Also, a regularization technique based on graphical distance is introduced that helps with stabilizing the predictions at nodes far from the boundary.

翻译：本文提出了一类带有狄利克雷和诺伊曼边界条件的图上的确定性系统辨识问题的通用框架。当沿边界存在控制节点时，我们采用先离散后优化的方法来估计最优控制。该架构的核心组件是我们提出的边界注入式消息传递神经网络，该网络能生成更精确且在边界附近具有显著稳定性的预测。此外，还引入了一种基于图距离的正则化技术，有助于稳定远离边界节点的预测结果。