GSOC Ideas

Implement Interval-based Reachability Methods

[TIRA](TIRA: Toolbox for Interval Reachability Analysis, by Pierre-Jean Meyer, Alex Devonport and Murat Arcak)

Recommended Skills:

Expected Results:

Mentors: Marcelo Forets.

---

Newtorks of Hybrid Systems

Recommended Skills:

Expected Results:

Mentors:

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

Hybrid Systems Interface to Simulink Models

Recommended Skills:

Expected Results:

Mentors:

https://github.com/nikos-kekatos/SL2SX

https://easychair.org/publications/open/V4

https://drive.google.com/file/d/0By5Nhm0s_V1cX0RMMEIyT2hRTVU/view

Reachability of Linear Partial Differential Equations

http://stanleybak.com/papers/tran2018adhs.pdf

Recommended Skills:

Expected Results:

Mentors:

Reachability of Differential-Algebraic Equations

Recommended Skills:

Expected Results:

Mentors:

---

Zonotope-based Neural Network Verification

Zonotopes are representations of extended use in set-based reachability analysis of dynamical systems, since linear transformations and Minkowski sums can be computed efficiently. However, they are are not closed under the intersection with a guard set hence it is needed to overappproximate the intersection with another other set type such as a polytope.

This project proposes to implement AI2: Safety and Robustness Certification of Neural Networks with Abstract Interpretation employing LazySets.jl to combine different set representations and operations between them.

Recommended Skills: Basic background on convex geometry and a taste for writing efficient code.

Expected Results: A working, efficient and documented implementation of AI2 using a combination of zonotopes and polytopes.

Mentors: Marcelo Forets and Christian Schilling.