Mining and visualizing recommendation spaces for elliptic PDEs with continuous attributes

In this paper we extend previous work in mining recommendation spaces based on symbolic problem features to PDE problems with continuous-valued attrib utes. We identify the research issues in mining such spaces, present a dyna mic programming algorithm from the data-mining literature, and describe how a priori domain metaknowledge can be used to control the complexity of ind uction. A visualization aid for continuous-valued recommendation spaces is also outlined. Two case studies are presented to illustrate our approach an d tools: (i) a comparison of an iterative and a direct linear system solver on nearly singular problems, and (ii) a comparison of two iterative solver s on problems posed on nonrectangular domains. Both case studies involve co ntinuously varying problem and method parameters which strongly influence t he choice of best algorithm in particular cases. By mining the results from thousands of PDE solves, we can gain valuable insight into the relative pe rformance of these methods on similar problems.