Surrogate-error-aware data assimilation strategies

Determine the most suitable filtering strategy for data assimilation with surrogate-model errors, including reduced-order-model errors, beyond the kriging-based bias-correction approach adopted in Opals.jl.

Background

The paper uses a kriging-based best linear unbiased predictor to estimate the observation-space bias induced when a computationally inexpensive reduced-order model replaces a full-order model in a Kalman-filter pipeline. The authors explicitly characterize this choice as provisional rather than definitive, because reduced-order-model errors may vary with the unknown parameters and may not be uniformly reduced in the full parameter-state space.

The numerical heat-equation experiment illustrates this limitation: kriging calibration improves accuracy in some observed quantities but does not necessarily improve every state variable or parameter estimate. Consequently, identifying a more generally effective strategy for accounting for surrogate-model error in data assimilation remains unresolved.

References

To this end, we adopt the approach of , though we note that this is more a working choice than a definitive strategy, since identifying the most suitable strategy for surrogate-error-aware \ac{da} remains an open question we intend to keep exploring.

— Opals.jl: a comprehensive, composable framework for data assimilation in Julia  (2608.24265 - Mueller, 25 Aug 2026) in Section 2, Subsection 2.5, “Incorporating reduced error models into the Kalman filter”