Learning Sparse Spatiotemporal Interaction Patterns in Nanoparticle Self-Assembly

Identifying the local interactions that drive the global structure in nanoparticle self-assembly from observations remains a significant challenge. We present a data-driven framework to learn interpretable, local interaction patterns directly from liquid-phase TEM videos. Our method discretizes the system into coarse-grained patches and learns the dynamics by optimizing for sparse linear operators within a sliding time window. This optimization, formulated on a manifold of sparse matrices, inherently encodes the spatial locality of interactions between neighboring patches. The resulting interaction matrices reveal explicit coupling mechanisms, such as orientational alignment (angle-to-angle) and aggregation/dispersion (density-to-density). Our framework quantifies the strength, spatial influence range, and temporal evolution of these coupling patterns. Validation via dynamics reconstruction confirms that our learned model accurately captures the emergent self-assembly behavior. This approach bridges data-driven discovery with mechanistic understanding, revealing how local patch-level rules generate complex global structures.