Data-driven Learning of Interaction Laws in Multispecies Particle Systems with Gaussian Processes: Convergence Theory and Applications

The article introduces an innovative Gaussian process framework aimed at learning interaction laws within multispecies particle systems by leveraging trajectory data. This approach extends previous convergence theory to accommodate more complex models, thereby enhancing the theoretical foundation for such learning methods. The framework demonstrates potential for multiscale modeling, where relatively simple interaction rules can give rise to complex emergent behaviors. By building on established methodologies, the work showcases how data-driven techniques can effectively capture the dynamics of heterogeneous particle systems. The convergence theory extension is a significant advancement, providing stronger guarantees for the learning process. Overall, the study highlights the applicability of Gaussian processes in modeling intricate multispecies interactions, suggesting promising avenues for future research in multiscale systems. This development aligns with ongoing efforts to integrate machine learning with physical system modeling.