Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis - Tagliapietra, Nicholas; Ensinger, Katharina; Zimmer, Christoph; Mian, Osman (Proceedings of the AAAI Conference on Artificial Intelligence, 2026)
Real world systems evolve in continuous-time according to their underlying causal relationships, yet their dynamics are often unknown. Existing approaches to learning such dynamics typically either discretize time ---leading to poor performance on irregularly sampled data--- or ignore the underlying causality. We propose CADYT, a novel method for causal discovery on dynamical systems addressing both these challenges. In contrast to state-of-the-art causal discovery methods that model the problem using discrete-time Dynamic Bayesian networks, our formulation is grounded in Difference-based causal models, which allow milder assumptions for modeling the continuous nature of the system. CADYT leverages exact Gaussian Process inference for modeling the continuous-time dynamics which is more aligned with the underlying dynamical process. We propose a practical instantiation that identifies the causal structure via a greedy search guided by the Algorithmic Markov Condition and Minimum Description Length principle. Our experiments show that CADYT outperforms state-of-the-art methods on both regularly and irregularly-sampled data, discovering causal networks closer to the true underlying dynamics.