Graph prolongation convolutional networks: explicitly multiscale machine learning on graphs with applications to...

Area of Science:

• Computational chemistry
• Machine learning
• Graph neural networks

Background:

• Graph convolutional networks (GCNs) are powerful tools for analyzing graph-structured data.
• Ensemble methods in GCNs can improve predictive accuracy but often come with increased computational cost.
• Predicting potential energy in molecular simulations is crucial for understanding material properties and chemical reactions.

Purpose of the Study:

• To introduce a novel ensemble graph convolutional network (GCN) model, the Graph Prolongation-Convolutional Network (GPN).
• To enhance the prediction accuracy of potential energy for monomer subunits in coarse-grained simulations.
• To demonstrate computational efficiency gains through multi-scale learning and optimized training schedules.

Main Methods:

• Developed a novel ensemble GCN model utilizing optimized linear projection operators for inter-scale information aggregation.
• Calculated linear projection operators as infima of an objective function relating GCN structure matrices.
• Implemented multi-scale training schedules adapted from algebraic multigrid methods.
• Derived backpropagation rules for network input with respect to output.

Main Results:

• The proposed Graph Prolongation-Convolutional Network (GPN) model demonstrated superior performance compared to other GCN ensemble models.
• Significant performance gains were quantified in terms of reduced Floating Point OPerations (FLOPs) and wall-clock time.
• Investigated and quantified computational benefits of various multi-scale training schedules.
• Compared the GPN model against a baseline with optimized graph coarsening.

Conclusions:

• The GPN model offers a computationally efficient and accurate approach for predicting potential energy in coarse-grained simulations.
• Multi-scale learning and optimized training schedules contribute to substantial computational savings.
• The developed backpropagation rules pave the way for extending the method to larger graph structures.