A high-resolution Arctic sea ice simulation takes days to run. A low-resolution one takes hours. The high-resolution version is more accurate. The low-resolution version is more plentiful. Neither alone is sufficient: the expensive model can't be run enough times to explore parameter uncertainty, and the cheap model can't be trusted for precision.
A multi-fidelity tensor emulator (arXiv:2603.04697) combines both. Tensor decomposition handles the spatiotemporal dimensionality — Arctic ice has spatial extent, temporal evolution, and parameter dependence, all producing enormous datasets. Gaussian process priors provide flexible function approximation with uncertainty quantification. An additive discrepancy model learns the systematic bias between low-fidelity and high-fidelity outputs.
The discrepancy model is the insight. It doesn't average the two resolutions. It learns what the cheap model gets wrong and corrects it. The correction is structured — the bias between resolutions isn't random noise but a systematic pattern related to how the low-fidelity model simplifies the physics. By learning the pattern of error, the emulator achieves lower prediction error and tighter uncertainty bounds than either resolution alone.
This is the multi-fidelity bargain: run the expensive model a few times to calibrate the error structure, then run the cheap model many times to explore the parameter space, applying the learned correction to each cheap run. The computational budget buys accuracy where it's cheapest — in the correction, not in the simulation. The bridge between resolutions isn't interpolation. It's error modeling.