Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networks

ICLR 2026 Conference Submission20261 Authors

Keywords: Equation Discovery, Kolmogorov-Arnold Networks, Graph Dynamical System, Interpretable AI, Network Dynamics, AI4Science

TL;DR: ML-driven equation discovery of graph dinamical systems, with a fair comparison and focus on interpretable models (KAN).

Abstract: The discovery of symbolic governing equations is a central goal in science, yet it remains a formidable challenge, in particular for graph dynamical systems where the network topology further shapes the system behavior. While artificial intelligence offers powerful tools for modeling these dynamics, the field lacks a rigorous, comparative benchmark to assess the true scientific utility of the discovered laws. This work establishes the first rigorous benchmark for this task, moving beyond simple fitting metrics to evaluate discovered laws on their long-term stability and, critically, their out-of-distribution generalization to unseen graph topologies. We introduce the Graph Kolmogorov-Arnold Network (GKAN-ODE), an architecture tailored for this domain, and propose a structure-aware symbolic regression method to leverage its inherent interpretability. Across a suite of synthetic and real-world graph dynamical systems, we demonstrate that symbolic models extracted from neural architectures, particularly our GKAN-ODE, achieve state-of-the-art performance and generalize to unseen networks, significantly surpassing existing baselines. This work presents the first systematic benchmark in this domain, clarifying the expressivity-interpretability trade-offs and offering a pathway from observational data to fundamental physical understanding, providing a critical new tool for data-driven discovery in network science.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 20261