Brian C. Williams, Olivier Raiman
Many physical phenomena are sufficiently complex that the corresponding equations afford little insight, or no analytical method provides an exact solution. Decompositional modeling (DM) captures a modeler' s tacit skill at solving non-linear algebraic systems. DM divides statespace into a patchwork of simpler subregimes, called caricatures, each of which preserves only the dominant characteristics of that regime. It then solves the simpler nonlinear system and identifies its domndn of validity. The varying patchwork reflects how variations in the parameters change the dominant characteristics. The patchwork is built by extracting equational features consisting of the relative strength of terms, and then exagerating and merging these features in different combinations, resulting in the different caricatural regimes. DM operates by providing strategic guidance to a pair of symbolic manipulation systems for qualitative sign and order of magnitude algebra. The approach is sufficient to replicate a broad set of examples from acid-base chemistry.