Generative Refinement Learning for Temporal Interpolation in Scientific Machine Learning
Abstract
Computationally expensive simulations and real-world observations often provide data at a lower temporal resolution than downstream tasks require. Averaging observations at fixed grid points can introduce errors, and motion estimates alone do not determine how the physical field values change. In this work, we study whether learning to correct a simple numerical interpolation improves the reconstruction of intermediate scientific fields. Our model, interpolative FLow EXpert (iFLEX), first estimates the missing field by taking a weighted average of the two observations at each grid point, giving more weight to the observation closer to the requested time. During training, subtracting this estimate from an observed intermediate field gives the residual that a conditional diffusion model learns to generate. Both observations condition the model, together with the target time, the interval between observations, and available physical parameters. To reconstruct an unobserved intermediate field, the generated residual is added to the weighted average. We evaluate iFLEX on Navier-Stokes Kraichnan turbulence, Shanghai radar precipitation, and sea surface temperature. Across these datasets, iFLEX achieves lower reconstruction error than the evaluated baselines, including optical-flow and diffusion models developed for video frame interpolation in computer vision. In a controlled turbulence comparison at a Reynolds number of 36,000, learning the residual reduces relative Frobenius norm error from about 13.7 for direct field generation to 10.5, with the diffusion backbone and training setup held fixed. Code is available at https://github.com/paulpuren/iflex.
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BibTeX
@misc{ren2026generative,
title = {{Generative Refinement Learning for Temporal Interpolation in Scientific Machine Learning}},
author = {Pu Ren and Michael W. Mahoney and N. Benjamin Erichson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36751},
eprint = {2610.36751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36751},
}
RIS
TY - UNPB
TI - Generative Refinement Learning for Temporal Interpolation in Scientific Machine Learning
AU - Pu Ren
AU - Michael W. Mahoney
AU - N. Benjamin Erichson
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36751
UR - https://arxiv.org/abs/2610.36751
AB - Computationally expensive simulations and real-world observations often provide data at a lower temporal resolution than downstream tasks require. Averaging observations at fixed grid points can introduce errors, and motion estimates alone do not determine how the physical field values change. In this work, we study whether learning to correct a simple numerical interpolation improves the reconstruction of intermediate scientific fields. Our model, interpolative FLow EXpert (iFLEX), first estimates the missing field by taking a weighted average of the two observations at each grid point, giving more weight to the observation closer to the requested time. During training, subtracting this estimate from an observed intermediate field gives the residual that a conditional diffusion model learns to generate. Both observations condition the model, together with the target time, the interval between observations, and available physical parameters. To reconstruct an unobserved intermediate field, the generated residual is added to the weighted average. We evaluate iFLEX on Navier-Stokes Kraichnan turbulence, Shanghai radar precipitation, and sea surface temperature. Across these datasets, iFLEX achieves lower reconstruction error than the evaluated baselines, including optical-flow and diffusion models developed for video frame interpolation in computer vision. In a controlled turbulence comparison at a Reynolds number of 36,000, learning the residual reduces relative Frobenius norm error from about 13.7 for direct field generation to 10.5, with the diffusion backbone and training setup held fixed. Code is available at https://github.com/paulpuren/iflex.
ER -