A0689
Title: Oh SnapMMD! Forecasting stochastic dynamics beyond the Schrodinger bridge's end
Authors: Renato Berlinghieri - Massachusetts Institute of Technology (United States) [presenting]
Abstract: Scientists often need to predict system behavior beyond the time window covered by snapshot data governed by latent stochastic dynamics. In single-cell mRNA profiling, for instance, transcriptional states are observed from different replicates at discrete times, but each measurement destroys the cell, so an individual cell's full trajectory is never seen. Yet, researchers want to forecast outcomes (e.g., stem-cell differentiation) from early measurements. Schrodinger-bridge (SB) methods can interpolate between snapshots, but existing approaches either follow a predefined reference dynamic chosen before observing data or assume a fixed, state-independent volatility by minimizing a Kullback-Leibler divergence, both of which can hurt forecasting accuracy. SnapMMD is introduced, a framework that learns latent dynamics by jointly fitting the distribution of observed states and their sampling times using a maximum mean discrepancy (MMD) loss. Unlike prior work, SnapMMD infers unknown, state-dependent volatility directly from the data. In experiments on synthetic and real datasets, SnapMMD delivers more accurate forecasts than SB baselines. It naturally handles missing or partial state observations and provides an interpretable $R^2$-style diagnostic of fit quality. Furthermore, SnapMMD matches or exceeds state-of-the-art methods in interpolation tasks and velocity-field reconstruction across all tested scenarios.
