Modern advances in technology have led to the generation of ever-increasing amounts of quantitative data from biological systems, such as gene-expression snapshots of developing cell populations in a tissue, or geometric data of residue positions within a protein. Experimental observations are often limited to be partial, so information about the underlying process or structure must instead be inferred from data. Through its connection to the Schrödinger problem of large deviations for stochastic processes, we find that entropic optimal transport arises as a natural tool for reconstructing unobserved cellular trajectories under precise assumptions. We develop both a theoretical and computational framework for inferring cellular dynamics based on optimal transport, and demonstrate its potential to extract the genetic logic underlying biological dynamics. In another vein, we also discuss the utility of generalized notions of optimal transport for matching and summarizing topological features in geometric structures such as biomolecules.
Joint work with (the groups of) Prof. Geoffrey Schiebinger, Prof. Lénaïc Chizat and Prof. Michael Stumpf.