Title: History-Bootstrapped Autoregressive Flow Matching for Reconstructing Inverse Boiling Dynamics

Abstract:

Deriving complete spatiotemporal fields from limited data is a cornerstone of scientific inference, enabling applications ranging from atmospheric state estimation via satellite imagery to the recovery of fluid dynamics from visual records. When observational data is sparse, the associated inverse problem becomes inherently ill-posed. Even if the governing partial differential equation (PDE) dynamics are Markovian within the full state space, the act of partial observation creates a non-Markovian posterior distribution that cannot be accurately resolved using information from a single time step alone.

To address this challenge, we introduce History-Bootstrapped Autoregressive Flow Matching (HB-ARFM), a novel framework designed for spatiotemporal inverse reconstruction under conditions of partial observability. This approach leverages historical observation data to bootstrap the initial reconstruction through conditional flow matching, thereby significantly reducing inherent ambiguities. Subsequently, the same conditional transport model is deployed in an autoregressive manner. By conditioning on both incoming observations and previous predictions, the model effectively propagates the reconstruction forward in time.

We assessed the efficacy of HB-ARFM by applying it to the reconstruction of boiling dynamics, specifically aiming to recover full velocity and temperature fields based solely on interface geometry and motion data. In evaluations involving two distinct inverse tasks characterized by varying levels of observation sparsity, HB-ARFM successfully generated reconstructions that were both physically consistent and temporally valid, outperforming existing models that failed to achieve such results.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC