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

Source: [(HB-ARFM) History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction](<https://www.sota2.com/research/paper/6a1e63b5dbd7150506f852a7>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-02T05:00:51.557Z

Authors: Xianwei Zou, Sheikh Md Shakeel Hassan, Arthur Feeney, Aparna Chandramowlishwaran

Published: 2026-05-29T20:39:28.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Velocity Reconstruction on Subcooled pool boiling (50 random snapshots)](<https://www.sota2.com/research/sota/velocity-reconstruction-on-subcooled-pool-boiling-50-random-snapshots.md>): Velocity Reconstruction; Subcooled pool boiling (50 random snapshots); Vel. Relative L2 Error: 0.747.

- [Temperature Reconstruction on Subcooled Pool Boiling Task 1 (50 random snapshots)](<https://www.sota2.com/research/sota/temperature-reconstruction-on-subcooled-pool-boiling-task-1-50-random-snapshots.md>): Temperature Reconstruction; Subcooled Pool Boiling Task 1 (50 random snapshots); Relative L2 Error (Temp): 3.3.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2606.00349>)

[PDF](<https://arxiv.org/pdf/2606.00349.pdf>)