(HB-ARFM) History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction
This work addresses the ill-posed inverse problem of reconstructing spatiotemporal fields from partial observations, which is fundamental to scientific inference in domains like atmospheric science and fluid dynamics.
HB-ARFM reconstructs spatiotemporal fields from partial observations by using observation history to bootstrap initial reconstruction and autoregressive flow matching to propagate forward, achieving physically valid reconstructions in boiling dynamics where other models fail.
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, reducing 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.