The exploration of the HPD region would be required regardless of the thermodynamic calculation method used, so it is worth mentioning how well each method compares when examining the raw time needed to get the initial estimates. The cost of the DFT calculations on Rhodium was about 1,500 GPU hours and 10,600 CPU hours, and the cost of the DFT calculations on Platinum for LSR fitting was about the 1,200 GPU hours and 8,000 CPU hours. In comparison, the expense of the ML predictions can be essentially neglected, as they can give a structure and energy in minutes with minimal resources. Considering the convergence of BPE to a similar optimized model across all three estimation methods, using ML-aided estimation is considerably more e cient. While some species will require DFT calibration, initiating from ML estimates serves as a valuable starting point, o↵ering substantial time and computational resource savings.