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

Researchers introduce History-Bootstrapped Flow Matching (HB-ARFM), a machine learning method for reconstructing complete spatiotemporal fields from partial observations, demonstrating particular success in recovering velocity and temperature fields from limited boiling dynamics data. The approach addresses a fundamental challenge in scientific inference where incomplete observations create ill-posed inverse problems that traditional single-timestep models cannot solve.

HB-ARFM tackles a critical problem in computational science: reconstructing full physical states when only fragmentary measurements are available. This challenge spans multiple domains, from meteorology to fluid dynamics, where complete sensor coverage is economically or technically infeasible. The proposed method leverages conditional flow matching—a generative modeling technique—to handle the non-Markovian nature of partially observed systems, where future states depend on historical information beyond the immediate previous timestep.

The technical innovation lies in a two-stage approach: first using observation history to bootstrap initial reconstructions via conditional flow matching, then applying the same transport model autoregressively by conditioning on both new observations and prior predictions. This architecture acknowledges that incomplete observations induce temporal dependencies that single-frame models fundamentally cannot capture.

For scientific computing and simulation communities, this advancement carries substantial implications. Many real-world systems operate under partial observability constraints, making accurate field reconstruction essential for digital twins, surrogate modeling, and physics-informed machine learning. The boiling dynamics application is particularly relevant, as thermal-fluid systems are difficult to fully instrument in experimental settings.

The research demonstrates practical value by achieving physically and temporally valid reconstructions across varying observation sparsity levels, where baseline approaches fail entirely. This success suggests potential deployment in industrial thermal management, climate modeling, and engineering design optimization. Future work will likely explore scalability to higher-dimensional problems and integration with domain-specific physics constraints.

• →HB-ARFM successfully reconstructs complete spatiotemporal fields from partial observations by leveraging observation history and autoregressive conditioning.
• →The method addresses the non-Markovian posterior induced by incomplete observations, a fundamental limitation of single-timestep models.
• →Demonstrated effectiveness on boiling dynamics, recovering full velocity and temperature fields from only interface geometry and motion data.
• →Conditional flow matching architecture enables temporal propagation that maintains physical validity across multiple prediction steps.
• →Approach has broad applicability across scientific inference domains where complete sensor coverage is impractical or impossible.