Intelligence in scientific computing
Communications of the ACM
Understanding complex dynamics by visual and symbolic reasoning
Artificial Intelligence - Special issue: Qualitative reasoning about physical systems II
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
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Understanding flow in the three-dimensional phase space is challenging both to human experts and current computer science technology. To break through the barrier, we are building a program called PSX3 that can autonomously explore the flow in a three-dimensional phase space, by integrating AI and numerical techniques. In this paper, I point out that quasi-symbolic representation called flow mappings is effective as a means of capturing qualitative aspects of three-dimensional flow and present a method of generating flow mappings for a system of ordinary differential equations with three unknown functions. The method is based on a finding that geometric cues for generating a set of flow patterns can be classified into five categories. I demonstrate how knowledge about interaction of geometric cues is utilized for intelligently controlling numerical computation.