New AI method jointly discovers network structure and dynamics from particle data

A new paper on arXiv (2606.18279) tackles the inverse problem of simultaneously learning both the network structure and the underlying dynamics of stochastic interacting particle systems. The authors, Demao Liu, Ting Gao, and Jinqiao Duan, propose two alternating least-squares estimators: a three-block scheme (TALS) and an integrated diagonal-augmented scheme (IALS). The IALS approach is particularly effective when node-specific local dynamics share a common functional form with node-dependent scaling, as it merges local and interaction coefficient updates into a single least-squares subproblem. The work establishes an identifiability result under a rank-2 joint coercivity condition with appropriate normalization, ensuring that the recovered graph and dynamics are unique.

Synthetic experiments demonstrate that both TALS and IALS accurately recover the interaction graph and dynamical components, remaining robust under stochastic forcing, observation noise, and basis mismatch. A real-data application on ictal SEEG recordings—intracranial EEG during epileptic seizures—shows that the learned models produce stable and interpretable dynamical summaries across multiple basis configurations. This scalable, theoretically grounded framework has broad potential for data-driven discovery in computational biology, neuroscience, and other fields where systems of interacting particles are observed, enabling researchers to infer hidden connectivity and dynamics from noisy trajectory data alone.