Establish whether the particle-swarm optimization reaches the global loss minimum

Determine whether the parameters obtained from the single finite-budget particle-swarm optimization run represent the global minimum of the machine-learning correction’s training loss.

Background

Each parent functional is trained once using a particle-swarm optimization procedure with a population of 100 and a budget of 3000 function evaluations in a 940-dimensional parameter space. The authors retain this protocol to reproduce the prior work, but they do not assess convergence to the global minimum or variation across random seeds.

The resulting loss reductions differ substantially among parent functionals, especially between B3LYP and r²SCAN. Since only one optimization run is performed for each model, the paper cannot determine whether the final parameters reflect a genuine global optimum or limitations of the finite optimization budget.

References

Thus, the optimization produces a substantially larger relative reduction in the loss for B3LYP than for r$2$SCAN. This difference is consistent with the smaller initial training-set errors of r$2$SCAN, although the single optimization run does not allow us to determine whether the resulting parameters represent the global minimum of the loss function.

— What Does a Semilocal Machine-Learning Correction Actually Learn? Size-Dependent Errors across Four Parent Functionals  (2609.37571 - Bhattacharjee et al., 29 Sep 2026) in Section 3, subsection “Training”