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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00349 |
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| _version_ | 1866918532564910080 |
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| author | Zou, Xianwei Hassan, Sheikh Md Shakeel Feeney, Arthur Chandramowlishwaran, Aparna |
| author_facet | Zou, Xianwei Hassan, Sheikh Md Shakeel Feeney, Arthur Chandramowlishwaran, Aparna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00349 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | (HB-ARFM) History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction Zou, Xianwei Hassan, Sheikh Md Shakeel Feeney, Arthur Chandramowlishwaran, Aparna Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science 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. |
| title | (HB-ARFM) History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction |
| topic | Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2606.00349 |