Reconstructing noisy intracellular expression dynamics using neural stochastic differential equations, Part I: Mathematical methods

We provide an analysis of the squared Wasserstein-2 distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared distance-based loss function in the reconstruction of SDEs from noisy trajectory data. To demonstrate the practicality of our Wasserstein distance-based loss

functions, we performed numerical experiments that demonstrate the efficiency of our method in reconstructing SDEs that may arise across many problems in cell biology.