Generalization of learned reconstruction (deconvolution) operators across regimes and discretizations

Determine how neural network-based reconstruction (deconvolution) operators R_θ that map a reduced field q̄ to a reconstructed full field u generalize across different physical regimes, numerical schemes, and discretizations when used for closure modeling by applying the original high-fidelity model F to R_θ(q̄).

Background

The paper discusses a reconstruction-based approach to closure in which a learned operator R_θ reconstructs the full field u from the reduced field q̄, enabling application of the original governing model F to the reconstructed state. Such reconstruction (also termed deconvolution) is an ill-posed inverse problem, for which recent machine learning methods have shown promise over classical approximate deconvolution.

However, the authors explicitly note that a key unresolved issue is whether these data-driven reconstruction operators can robustly generalize when the physical regime, numerical scheme, or discretization changes. This limits the portability and reliability of learned reconstructions for practical multiscale simulations.