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UID:20251106T183746EST-08453iLaUl@132.216.98.100
DTSTAMP:20251106T233746Z
DESCRIPTION:Title: Deep learning of conjugate mappings\n\nAbstract: Despite
  many of the most common chaotic dynamical systems being continuous in tim
 e\, it is through discrete time mappings that much of the understanding of
  chaos is formed. Henri Poincaré first made this connection by tracking co
 nsecutive iterations of the continuous flow with a lower-dimensional\, tra
 nsverse subspace. The mapping that iterates the dynamics through consecuti
 ve intersections of the flow with the subspace is now referred to as a Poi
 ncaré map\, and it is the primary method available for interpreting and cl
 assifying chaotic dynamics. Unfortunately\, in all but the simplest system
 s\, an explicit form for such a mapping remains outstanding. In this talk 
 I present a method of discovering explicit Poincaré mappings using deep le
 arning to construct an invertible coordinate transformation into a conjuga
 te representation where the dynamics are governed by a relatively simple c
 haotic mapping. The invertible change of variable is based on an autoencod
 er\, which allows for dimensionality reduction\, and has the advantage of 
 classifying chaotic systems using the equivalence relation of topological 
 conjugacies. We illustrate with low-dimensional systems such as the Rössle
 r and Lorenz systems\, while also demonstrating the utility of the method 
 on the infinite-dimensional Kuramoto--Sivashinsky equation. \n\nTo registe
 r contact : appliedseminars [at] math.mcgill.ca\n\nWeb site : https://dms.
 umontreal.ca/~mathapp/\n
DTSTART:20211004T200000Z
DTEND:20211004T210000Z
SUMMARY:Jason Bramburger (George Mason University)
URL:/mathstat/channels/event/jason-bramburger-george-m
 ason-university-333793
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