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.