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Fix return times function for continuous systems #278

Merged
merged 17 commits into from
Sep 24, 2022
Merged

Fix return times function for continuous systems #278

merged 17 commits into from
Sep 24, 2022

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Datseris
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@Datseris Datseris commented Sep 18, 2022 •
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This PR aims to:

  1. Improve source code clarity of return times for discrete systems
  2. Overall better organize tests for return times
  3. Fix return times for continuous systems, which never really worked well and was also super slow. To this end we have
    • Re-written the source code from scratch.
    • Offer two algoritms: linear interpolation, or integrator-based interpolation with minimization for finding closest point and then rootfinding for finding the crossings.
    • Linear interpolation works only for spheres (in the future one could contribute code for rectangle crossing I guess.
    • High precision interpolation uses Optim.jl and Roots.jl.
    • Serious tests are now also done for continuous systems.
  4. Performance increase for continuous systems: TODO; write by how much.

Only todo left is to make it work for hyperrectangles in continuous systems.

@Datseris Datseris added the rare-events Rare events and extreme values label Sep 19, 2022
Datseris
Datseris commented Sep 23, 2022
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src/rareevents/mean_return_times/mrt_continuous.jl
Comment on lines +180 to +191
import Optim, Roots
function closest_trajectory_point(integ, u0, metric, method::CrossingAccurateInterpolation)
# use Optim.jl to find minimum of the function
f = (t) -> evaluate(metric, integ(t), u0)
# Then find minimum of `f` in limits `(tprev, t)`
optim = Optim.optimize(
f, integ.tprev, integ.t, Optim.Brent();
store_trace=false, abs_tol = method.abstol, rel_tol = method.reltol,
)
tmin, dmin = Optim.minimizer(optim), Optim.minimum(optim)
return tmin, dmin
end
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@KalelR here is the code snippet

@Datseris Datseris merged commit 61667b4 into main Sep 24, 2022
@Datseris Datseris deleted the mean_return_time branch September 24, 2022 17:58
This was referenced Sep 24, 2022
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