Reproduce “Learning Dynamics and Structure of Complex Systems Using Graph Neural Networks” on OpenResearch

About this paper

Zhe Li, Andreas S. Tolias, Xaq Pitkow

The graph translator connects a GNN’s instance-specific parameters to Gaussian graphical model structure. The authors train shared update rules across 36 systems and map node and edge parameters to precision-matrix attributes. On held-out graphs, it predicts local precision and coupling with R² scores of 0.946 and 0.867; on a new system, translated parameters produce credible BP traces without trace training.

Key insights

• L2 regularization on GNN structural parameters is critical for disentangling universal dynamics from specific structural attributes, leading to interpretable, low-dimensional manifolds in the parameter space.
• The learned GNN states and messages form low-dimensional manifolds where positions along these manifolds correlate directly with the underlying system's static attributes.
• Nonlinearity in the message function is crucial for GNNs to accurately fit complex nonlinear dynamics, and a non-zero edge dimension is necessary to model interaction strengths.

Summary by alphaXiv.