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GSOC Ideas
Zonotopes are representations of extended use in set-based analysis, since linear transformations and Minkowski sums can be computed efficiently. However, they are are not closed under intersections. In the literature there exist different alternatives for overapproximation of zonotopes intersections with other set types. The set library LazySets.jl already offers support for zonotopes but lacks some of the state-of-the-art methods.
Applications of this project are in verification of hybrid dynamical systems (see juliareach.org) and in verification of neural networks AI2 employing LazySets.jl (see NeuralVerif).
Recommended Skills: A background on convex geometry and a taste for writing efficient code.
Expected Results: Zonotope intersections and operations between them. Some possibilities are: order reduction metods, zonotope intersections, Minkowski difference of zonotopes.
Mentors: Marcelo Forets and Christian Schilling.
[TIRA](TIRA: Toolbox for Interval Reachability Analysis, by Pierre-Jean Meyer, Alex Devonport and Murat Arcak)
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Mentors: Marcelo Forets.
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https://dl.acm.org/citation.cfm?id=2883826&dl=ACM&coll=DL
https://drive.google.com/file/d/0By5Nhm0s_V1cUmE5UUdaV044NlE/view
http://spaceex.imag.fr/sites/default/files/introduction_to_spaceex_0.pdf
https://ths.rwth-aachen.de/wp-content/uploads/sites/4/technical-report.pdf
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https://github.com/nikos-kekatos/SL2SX
https://easychair.org/publications/open/V4
https://drive.google.com/file/d/0By5Nhm0s_V1cX0RMMEIyT2hRTVU/view
http://stanleybak.com/papers/tran2018adhs.pdf
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