  The Cluster Expansion (CE) Method encounters significant computational
challenges in multicomponent systems due to the computational expense of
generating training data through density functional theory (DFT) calculations.
This work aims to refine the cluster and structure selection processes to
mitigate these challenges. We introduce a novel method that significantly
reduces the computational load associated with the calculation of fitting
parameters. This method employs a Graph Neural Network (GNN) model, leveraging
the M3GNet network, which is trained using a select subset of DFT calculations
at each ionic step. The trained surrogate model excels in predicting the volume
and energy of the final structure for a relaxation run. By employing this
model, we sample thousands of structures and fit a CE model to the energies of
these GNN-relaxed structures. This approach, utilizing a large training
dataset, effectively reduces the risk of overfitting, yielding a CE model with
a root-mean-square error (RMSE) below 10 meV/atom. We validate our method's
effectiveness in two test cases: the (Cr,Hf,Mo,Ta,Ti,Zr)B$_2$ diboride system
and the Refractory High-Entropy Alloy (HEA) AlHfNbTaTiZr system. Our findings
demonstrate the significant advantages of integrating a GNN model, specifically
the M3GNet network, with CE methods for the efficient predictive analysis of
chemical ordering in High Entropy Materials. The accelerating capabilities of
the hybrid ML-CE approach to investigate the evolution of Short Range Ordering
(SRO) in a large number of stoichiometric systems. Finally, we show how it is
possible to correlate the strength of chemical ordering to easily accessible
alloy parameters.
