Automated phase portrait analysis by integrating qualitative and quantitative analysis
Toyoaki Nishida, K. Mizutani, Atsushi Kubota, Shuji Doshita · National Conference on Artificial Intelligence · 1991
It has been widely believed that qualitative analysis guides quantitative analysis, while sufficient study has not been made from technical viewpoints. In this paper, we present a case study with PSX2NL, a program which autonomously analyzes the behavior of two-dimensional nonlinear differential equations, by integrating knowledge-based methods and numerical algorithms. PSX2NL focuses on geometric properties of solution curves of ordinary differential equations in the phase space. PSX2NL is designed based on a couple of novel ideas: (a) a set of flow mappings which is an abstract description of the behavior of solution curves, and (b) a flow grammar which specifies all possible patterns of solution curves, enabling PSX2N L to derive the most plausible interpretation when complete information is not available. We describe the algorithms for deriving flow mappings.