Mingtao Xia, NewYork University
In this talk, i will introduce two novel wasserstein-distance-based uncertainty quantification methods i developed for aiming at quantifying intrinsic fluctuations and extrinsic noise with applications in reconstructing noisy single-cell molecular dynamics. The methods i shall discuss include: i) a time-decoupled squared wasserstein-2 method for efficient training of neural stochastic differential equations as surrogate models for approximating stochastic processes that capture intrinsic fluctuations of intracellular protein and mrna counts over time and ii) a local squared wasserstein-2 method for reconstructing uncertain models with latent variables or uncertain parameters, which aim to quantify heterogeneities among cells.