Graph Neural Networks (GNNs) are one of the architectures used in Physics-Informed Machine Learning and a powerful tool for modeling graph-structured systems. From a physical perspective, such systems are not solely governed by topological structure; boundary conditions play an important role in determining system dynamics. However, conventional GNNs are unable to incorporate boundary conditions explicitly. We propose a graph representation and its Laplacian matrix with boundary conditions and develop a GNN framework that ccounts for boundary effects. We demonstrate the effectiveness of our GNN model through electrical circuit datasets.
Track ID:
2.1
Track Name:
Neural Networks, Learning and Artificial Intelligence
