Fast equivalent operational model

The functional form of the HDMR expansion and its use for global sensitivity analysis was aheady discussed in Sect. 5.5.5, but a similar approach can also be taken to develop reduced model representations. The purpose is to create a fast equivalent operational model (FEOM) based on the HDMR, giving sufficient accuracy with respect to the full chemical model, but with much lower computational expense. HDMR builds approximations recursively, based on the assumption that high-order-correlated effects of the inputs are expected to have negligible impact on the output. Applications have shown that the order of the correlations between the independent variables dies off rapidly, and therefore, only a few terms are usually required to represent even highly nonlinear input-output relationships. 

Wang, S.W., Balakrishnan, S., Georgopoulos, P. Fast equivalent operational model of tropospheric alkane photochemistry. AIChE J. 51, 1297-1303 (2005)... 

We can now use our projection technique to recover averaged time evolution operators in which some of the system coordinates are considered as fast. An interesting case is given by the model in which the solvent polarization relaxes faster than the reorientational molecular modes, that is, the equivalent of equation (1.16). Note that now the matrices Uj 2 (where the subscripts 1, 2 imply we are referring to both U, and U2), are simply given by (-sin (, 2, cos <, 2)" and the resulting diagonal elements of the final friction matrix are constant, so... 

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