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[Submitted on 9 Jun 2023 (v1), last revised 20 Dec 2023 (this version, v2)]

Title:A Graph Dynamics Prior for Relational Inference

Authors:Liming Pan, Cheng Shi, Ivan Dokmanić
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Abstract: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 this https URL.
Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as: arXiv:2306.06041 [cs.LG]
  (or arXiv:2306.06041v2 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2306.06041
arXiv-issued DOI via DataCite

Submission history

From: Liming Pan [view email]
[v1] Fri, 9 Jun 2023 17:07:04 UTC (2,275 KB)
[v2] Wed, 20 Dec 2023 06:58:35 UTC (1,608 KB)
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