Rigorous global-convergence analysis of the optimization procedure

Prove rigorous global-convergence guarantees for the differential-evolution search and local polishing procedures used by Weak-Pareto for fractional-order and support discovery.

Background

Weak-Pareto uses differential evolution to search continuous fractional orders and local gradient-free polishing to refine the selected model. These procedures are described as heuristic, so the empirical recovery results do not establish convergence to a globally optimal model. A rigorous analysis of global convergence is explicitly identified as an unresolved problem.

References

The differential-evolution search and local polishing are heuristic optimisation procedures, and rigorous global-convergence analysis is left for future work.

— Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection  (2608.12879 - Thanasutives et al., 13 Aug 2026) in Section 6, Limitations and future work