# Intersection of \`SciMLBase.EnsembleSolution\`s

**URL:** <https://discourse.julialang.org/t/intersection-of-scimlbase-ensemblesolution-s/67390>\
**Category:** Numerics\
**Tags:** question, package, diffeq\
**Created:** [August 31, 2021, 12:32am UTC](https://discourse.julialang.org/t/intersection-of-scimlbase-ensemblesolution-s/67390 "2021-08-31T00:32:32Z")\
**Posts on this page:** 1\
**Showing post:** 7

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**Author:** ![cadojo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cadojo/32/25328_2.png) [@cadojo](https://discourse.julialang.org/u/cadojo)\
**Post date:** [September 1, 2021, 4:22am UTC](https://discourse.julialang.org/t/intersection-of-scimlbase-ensemblesolution-s/67390/7 "2021-09-01T04:22:33Z")

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I was thinking about looking into reachability analysis, especially after seeing the JuliaCon 2021 workshop / content.

I understand that set propagation is scalable for linear systems, and numerical integration is scalable for nonlinear systems. These dynamics are nonlinear, and while I don’t know if they formally fit the definition of “chaotic dynamics”, they are certainly extremely sensitive to initial conditions. I’m a bit concerned that I’ll need a level of precision that set propagation won’t be able to provide (but like I said, I’m definitely going to try, if for no other reason than as an excuse to play around with `ReachabilityAnalysis.jl`).

The point about convexification is really interesting — I wasn’t aware that capability existed / was used. @mforets are you aware of any Julia implementations which “convexify” a discrete set? I searched a bit, but haven’t found any.

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