A Graph Dynamics Prior for Relational Inference
This work addresses a bottleneck in scientific machine learning by improving robustness to unknown sampling rates, making it suitable for real applications, though it is incremental as it builds on existing GNN-based methods.
The paper tackles the problem of relational inference in dynamical systems by proposing a graph dynamics prior (GDP) that uses error amplification in non-local polynomial filters to steer solutions to the ground-truth graph, resulting in far more accurate graph reconstruction with remarkable robustness to under-sampling compared to earlier methods.
Relational inference aims to identify interactions between parts of a dynamical system from the observed dynamics. Current state-of-the-art methods fit the dynamics with a graph neural network (GNN) on a learnable graph. They use one-step message-passing GNNs -- intuitively the right choice since non-locality of multi-step or spectral GNNs may confuse direct and indirect interactions. But the \textit{effective} interaction graph depends on the sampling rate and it is rarely localized to direct neighbors, leading to poor local optima for the one-step model. In this work, we propose a \textit{graph dynamics prior} (GDP) for relational inference. GDP constructively uses error amplification in non-local polynomial filters to steer the solution to the ground-truth graph. To deal with non-uniqueness, GDP simultaneously fits a ``shallow'' one-step model and a polynomial multi-step model with shared graph topology. Experiments show that GDP reconstructs graphs far more accurately than earlier methods, with remarkable robustness to under-sampling. Since appropriate sampling rates for unknown dynamical systems are not known a priori, this robustness makes GDP suitable for real applications in scientific machine learning. Reproducible code is available at https://github.com/DaDaCheng/GDP.