Generative Refinement Learning for Temporal Interpolation in Scientific Machine Learning

Pu Ren, Michael W. Mahoney, N. Benjamin Erichson

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…