Learning Stochastic Dynamics from Snapshots through Regularized Unbalanced Optimal Transport

Learn to reconstruct continuous stochastic dynamics from sparsely time-resolved snapshots using a novel deep learning approach based on regularized unbalanced optimal transport (RUOT) in this research presentation. Explore how this method models dynamics without requiring prior knowledge of growth and death processes, allowing these patterns to be learned directly from data. Discover the theoretical connections between RUOT and the Schrödinger bridge problem while examining key challenges and potential solutions in the field. Follow demonstrations of the method's effectiveness through applications to synthetic gene regulatory networks, high-dimensional Gaussian Mixture Models, and single-cell RNA-seq data from blood development. Compare this approach with existing methods to understand how it accurately identifies growth and transition patterns, eliminates false transitions, and constructs the Waddington developmental landscape for biological systems.