Artificial Intelligence - Special volume on qualitative reasoning about physical systems
Artificial Intelligence
Automatic qualitative analysis of dynamic systems using piecewise linear approximations
Artificial Intelligence
A qualitative simulation based method to construct phase portraits
A qualitative simulation based method to construct phase portraits
Higher Order Derivative Constraints and a QSIM-based Total Simulation Scheme
Higher Order Derivative Constraints and a QSIM-based Total Simulation Scheme
Taming intractible branching in qualitative simulation
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2
Extracting and representing qualitative behaviors of complex systems in phase spaces
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 2
A geometric approach to total envisioning
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 2
Qualitative reasoning and bifurcations in dynamic systems
MICAI'06 Proceedings of the 5th Mexican international conference on Artificial Intelligence
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We have developed and implemented in the QPORTRAIT program a qualitative simulation based method to construct phase portraits for a significant class of systems of two coupled first order autonomous differential equations, even in the presence of incomplete, qualitative knowledge. Differential equation models are important for reasoning about physical systems. The field of nonlinear dynamics has introduced the powerful phase portrait representation for the global analysis of nonlinear differential equations. QPORTRAIT uses qualitative simulation to generate the set of all possible qualitative behaviors of a system. Constraints on two-dimensional phase portraits from nonlinear dynamics make it possible to identify and classify trajectories and their asymptotic limits, and constrain possible combinations. By exhaustively forming all combinations of features, and filtering out inconsistent combinations, QPORTRAIT is guaranteed to generate all possible qualitative phase portraits. We have applied QPORTRAIT to obtain tractable results for a number of nontrivial dynamical systems. Guaranteed coverage of all possible behaviors of incompletely known systems complements the more detailed, but approximation-based results of recently-developed methods for intelligentlyguided numeric simulation [Nishida et al; Sacks; Yip; Zhao]. Combining the strengths of both approaches would better facilitate automated understanding of dynamical systems.