Generative Models Identify Dynamical System Separatrices

Researchers have developed a novel approach to tackle the challenge of identifying separatrices in high-dimensional, multistable dynamical systems. These boundaries dictate how systems transition between different states but are notoriously difficult to map due to their infrequent visitation during simulations. Traditional methods struggle with complexity and require prior system knowledge. The new framework integrates supervised classification with generative modeling. Initially, neural networks are trained to classify initial conditions based on their eventual basins of attraction. Areas where the classifier exhibits high uncertainty are then pinpointed as approximate separatrices. Subsequently, score-based generative models are trained specifically on data from these high-uncertainty regions. This allows for the generation of sample densities that accurately reflect the empirical distribution of points near the separatrix manifold, providing a systematic and data-driven way to reconstruct these critical structures.