(HB-ARFM) History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction

2026-05-29

AI Summary

Reconstructing spatiotemporal physical fields—such as velocity and temperature fields in boiling processes—from sparse partial observations is highly ill-posed, as the observation operator induces a non-Markovian posterior distribution, rendering single-step inference insufficient for accurate reconstruction. This work proposes a History-Guided Autoregressive Flow Matching method (HB-ARFM), which explicitly incorporates observational history into the flow matching framework for the first time. By initializing with conditional flow matching and autoregressively fusing new observations with historical predictions over time, HB-ARFM achieves temporally consistent full-field reconstructions. The method effectively mitigates ambiguity under partial observability and significantly outperforms existing approaches in two boiling inverse problems with varying sparsity levels, recovering physically plausible and temporally coherent velocity and temperature fields.

Abstract

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.

Problem

• inverse problem
• spatiotemporal reconstruction
• partial observability
• boiling dynamics
• ill-posed

Innovation

• history-bootstrapped
• autoregressive flow matching
• inverse reconstruction
• partial observability
• spatiotemporal dynamics