Mining and visualizing recommendation spaces for elliptic PDEs with continuous attributes

Abstract

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