Unsupervised Learning Approach to Wave-Packet Dynamics from Coupled Temporal-Spatial Correlations and Its Generative Extension

Understanding complex quantum dynamics in realistic materials requires insight into the underlying correlations that dominate the interactions between the participating particles. Due to the wealth of information involved in these processes, applying artificial intelligence (AI) methods is compelling. However, data-driven approaches typically focus on identifying maximum variations in data, rather than considering the correlations between them. Here, we present an approach that recognizes correlation patterns to explore convoluted dynamical processes. Our scheme uses singular value decomposition (SVD) to extract dynamical features, unveiling the internal temporal-spatial interrelations that generate the dynamical mechanisms. We apply our approach to study light-induced wave-packet propagation in organic crystals, of interest for applications in material-based quantum computing and quantum information science. We show how the transformation from the input momentum and time coordinates onto a new correlation-induced coordinate space allows direct recognition of the relaxation and dephasing components dominating the dynamics and demonstrates their dependence on the initial conditions. A tensor product state composed of a linear combination of singular vectors is proposed as a powerful method for generating new states that encapsulate the full spectrum of potential correlated spatial dynamics in the system. This approach enables the construction of new data that is consistent with the physical constraints and observed correlations, providing a more comprehensive representation of the underlying dynamics. By simulating physically feasible states, the tensor product approach, which goes beyond SVD analysis, offers a robust framework for exploring complex dynamical processes, significantly enhancing the impact of AI-based analysis in multicomponent systems, particularly where data samples are limited and challenging to acquire.