History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction

Reconstructing spatiotemporal fields from partial observations is fundamental to scientific inference, from inferring atmospheric states from satellite data to recovering fluid states from imaging. When observations are incomplete, the inverse problem is fundamentally ill-posed: even when the underlying PDE dynamics are Markovian in the full state, partial observation operators induce a non-Markovian posterior that cannot be resolved from a single timestep. We propose a history-bootstrapped autoregressive flow matching (HB-ARFM) for spatiotemporal inverse reconstruction under partial observability. Observation history bootstraps the initial reconstruction via conditional flow matching, resolving ambiguities. The same conditional transport model is then applied autoregressively, conditioning on both new observations and past predictions to propagate the reconstruction forward in time. We evaluate the method on boiling dynamics reconstruction, recovering full velocity and temperature fields from interface geometry and motion. Across two inverse tasks with varying observation sparsity, HB-ARFM produces physically and temporally valid reconstructions where other models fail.

Boiling is one of the most effective ways to remove heat, making it vital for cooling computer chips and data centers, generating power, and many other systems. But the quantities engineers care about most, like the temperature and flow of liquid right next to a hot surface, are nearly impossible to measure while bubbles rapidly form and rise. What we can easily capture is video showing where bubbles are and how their edges move. Can we recover the invisible temperature and motion from those images alone? A single snapshot is not enough, since many different hidden states could produce the same picture. Our key idea is to use a short window of recent frames, which narrows the possibilities, then step forward in time using our model's own past predictions to stay accurate over long sequences. Tested on simulated boiling, our method recovers realistic fields where existing approaches blur or break down.