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.

References

These methods can be considered an improvement over approximate deconvolution techniques because they do not need the assumption of an invertible filter, but open challenges include how such data-driven methods can generalize across physical regimes, numerical schemes, and discretizations.

— Scientific machine learning for closure models in multiscale problems: a review  (2403.02913 - Sanderse et al., 2024) in Section 3.3 (Reconstruction)

This is an architectural transfer property, not a claim of exact equality across resolutions or arbitrary array geometries. Approximation quality under a changed discretization remains an empirical question.

— GCNO: Gramian Chebyshev Neural Operator for Physics-Based Compression of Wireless Channels  (2608.18522 - Murshed et al., 19 Aug 2026) in Appendix B, Section "Neural-Operator Characterization"