Affine Lumping Formalism for Comparison of Projection-Based Model Reduction Techniques

Geoffrey Oxberry, Massachusetts Institute of Technology

Numerous methods exist for generating smaller, reduced chemical models from large, detailed chemical models. These methods arise from a variety of different theoretical backgrounds, yet few comparisons have been made between different model reduction methods. In order to assess the relative quality of these different model reduction techniques, these methods must be compared with each other using a common framework. As one element of such a framework, we propose a formalism called affine lumping that can be used to describe projection-based model reduction methods. This formalism defines two affine mappings. The first affine mapping is used to lump the state variables from a detailed model to a reduced model with reduced state variables. The second affine mapping is used to unlump the reduced state variables and lift the reduced model back into the original state space. Conditions are stated under which the application of these two affine mappings in succession yields a solution of the original model. Finally, the techniques of species lumping by Li et al., computational singular perturbation and reaction invariants are all cast as special cases of affine lumping, to illustrate the potential usefulness of the affine lumping formulation. Given that three different model reduction techniques can be recast using the affine lumping formalism, it is possible that other model reduction techniques may be also be special cases of affine lumping. The affine lumping formalism could then be used as a common standard against which different projection-based model reduction techniques can be compared in order to assess their relative quality.

Abstract Author(s): Geoffrey M. Oxberry, William H. Green, Paul I. Barton