Independent control of EC and MOR basis growth

Develop surrogate error metrics that track model-order-reduction convergence independently of eigenvector-continuation basis growth and directly control the reduced-order-model dimension while maintaining a specified accuracy.

Background

The MOR+EC construction currently couples the growth of the eigenvector-continuation basis to the growth of the model-order-reduction projection: every vector added to the EC basis contributes additional columns to the MOR projections. This coupling can improve accuracy but also enlarges the reduced model and diminishes the computational speedup.

The paper notes that surrogate error metrics could instead monitor convergence of the MOR resolvent independently from EC-basis growth and cap the reduced-model dimension directly. Such a strategy is left unresolved because the reported operating points already provide sufficiently small errors with substantial speedups.

References

That coupling is a choice, not a requirement: surrogate error metrics could track ROM convergence independently of $$'s growth and cap $m$ directly. We leave that for future work, since at the operating points used elsewhere in this paper -- an order of magnitude of speedup or more -- the present errors are already small.

— Compact representation of strongly correlated Green's functions: the MOR+EC way to explore phase space  (2609.28647 - Hogan et al., 23 Sep 2026) in Section 4.2, subsection “Accuracy and Cost”