Table 2 The 30 best combinations of scaling (\(w_u\) and \(w_p\)) and offset parameters (\(b_u\) and \(b_p\)) for \(\alpha =\beta =1\) based on the \(\mathscr {L}_2\) relative error by updating Table 1 with the results from a Bayes optimization.

\(3.18\textrm{e}{-}3\)

\(1.26\textrm{e}{-}2\)

\(9.86\textrm{e}{-}5\)

\(3.82\textrm{e}{-}4\)

\(8.69\textrm{e}{-}3\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}5}\)

\(\underline{1\textrm{e}{-}4}\)

\(\underline{1.00\textrm{e}{-}2}\)

\(1.01\textrm{e}{-}3\)

\(1.03\textrm{e}{-}2\)

\(2.98\textrm{e}{-}2\)

\(2.89\textrm{e}{-}3\)

\(1.04\textrm{e}{-}2\)

\(2.84\textrm{e}{-}3\)

\(2\textrm{e}{-}2\)

\(9.71\textrm{e}{-}4\)

\(3.22\textrm{e}{-}5\)

\(1.04\textrm{e}{-}2\)

\(2.92\textrm{e}{-}2\)

\(8.12\textrm{e}{-}3\)

\(2.78\textrm{e}{-}3\)

\(1.06\textrm{e}{-}1\)

\(1.04\textrm{e}{-}2\)

\(1.14\textrm{e}{-}3\)

\(1.55\textrm{e}{-}2\)

\(3.22\textrm{e}{-}2\)

\(3.65\textrm{e}{-}5\)

\(1.08\textrm{e}{-}2\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}3}\)

\(\underline{1\textrm{e}{-}1}\)

\(\underline{1.11\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}3}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}5}\)

\(\underline{1\textrm{e}{-}5}\)

\(\underline{1.14\textrm{e}{-}2}\)

\(1.11\textrm{e}{-}2\)

\(1.47\textrm{e}{-}2\)

\(1.45\textrm{e}{-}4\)

\(7.55\textrm{e}{-}2\)

\(1.14\textrm{e}{-}2\)

\(8.97\textrm{e}{-}3\)

\(4.58\textrm{e}{-}2\)

\(2.26\textrm{e}{-}2\)

\(5.37\textrm{e}{-}5\)

\(1.15\textrm{e}{-}2\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}3}\)

\(\underline{1\textrm{e}{-}5}\)

\(\underline{1\textrm{e}{-}1}\)

\(\underline{1.15\textrm{e}{-}2}\)

\(9.89\textrm{e}{-}3\)

\(9.35\textrm{e}{-}3\)

\(5.80\textrm{e}{-}3\)

\(1.16\textrm{e}{-}5\)

\(1.15\textrm{e}{-}2\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}4}\)

\(\underline{1\textrm{e}{-}5}\)

\(\underline{1.15\textrm{e}{-}2}\)

\(1.64\textrm{e}{-}3\)

\(5.61\textrm{e}{-}3\)

\(6.88\textrm{e}{-}4\)

\(3.43\textrm{e}{-}2\)

\(1.16\textrm{e}{-}2\)

\(6.03\textrm{e}{-}3\)

\(6.45\textrm{e}{-}3\)

\(1.88\textrm{e}{-}2\)

\(1.96\textrm{e}{-}4\)

\(1.17\textrm{e}{-}2\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}4}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1.18\textrm{e}{-}2}\)

\(9.42\textrm{e}{-}3\)

\(1.07\textrm{e}{-}2\)

\(4.33\textrm{e}{-}3\)

\(8.26\textrm{e}{-}5\)

\(1.18\textrm{e}{-}2\)

\(3.68\textrm{e}{-}3\)

\(6.51\textrm{e}{-}3\)

\(1.25\textrm{e}{-}2\)

\(1.18\textrm{e}{-}3\)

\(1.19\textrm{e}{-}2\)

\(6.77\textrm{e}{-}3\)

\(1.03\textrm{e}{-}2\)

\(1.44\textrm{e}{-}3\)

\(4.21\textrm{e}{-}5\)

\(1.19\textrm{e}{-}2\)

\(8.39\textrm{e}{-}4\)

\(3.23\textrm{e}{-}2\)

\(7.52\textrm{e}{-}3\)

\(2.96\textrm{e}{-}1\)

\(1.19\textrm{e}{-}2\)

\(5.62\textrm{e}{-}3\)

\(3.62\textrm{e}{-}3\)

\(1.65\textrm{e}{-}5\)

\(3.25\textrm{e}{-}5\)

\(1.19\textrm{e}{-}2\)

\(3.35\textrm{e}{-}3\)

\(2.86\textrm{e}{-}2\)

\(4.19\textrm{e}{-}2\)

\(2.82\textrm{e}{-}2\)

\(1.20\textrm{e}{-}2\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}3}\)

\(\underline{1.20\textrm{e}{-}2}\)

\(5.65\textrm{e}{-}3\)

\(1.04\textrm{e}{-}2\)

\(7.53\textrm{e}{-}4\)

\(1.39\textrm{e}{-}3\)

\(1.21\textrm{e}{-}2\)

\(2.51\textrm{e}{-}3\)

\(4.83\textrm{e}{-}3\)

\(6.53\textrm{e}{-}5\)

\(1.98\textrm{e}{-}5\)

\(1.22\textrm{e}{-}2\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}3}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1.22\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}5}\)

\(\underline{1\textrm{e}{-}5}\)

\(\underline{1.22\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}2}\)

\(\underline{1\textrm{e}{-}1}\)

\(\underline{1.22\textrm{e}{-}2}\)

\(4.51\textrm{e}{-}3\)

\(2.47\textrm{e}{-}3\)

\(5.90\textrm{e}{-}5\)

\(1.42\textrm{e}{-}3\)

\(1.22\textrm{e}{-}2\)

\(3.07\textrm{e}{-}2\)

\(2.46\textrm{e}{-}3\)

\(4.39\textrm{e}{-}2\)

\(3.86\textrm{e}{-}2\)

\(1.23\textrm{e}{-}2\)