gszep / bifurcationinference.jl Goto Github PK

learning state-space targets in dynamical systems

Home Page: https://github.com/gszep/BifurcationFit.jl/blob/master/docs/article.pdf

License: MIT License

Julia 100.00%

machine-learning dynamical-systems state-space kernel-density-estimation continuation pseudo-arclength-continuation differentiable-programming

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rveltz standardgalactic

bifurcationinference.jl's Issues

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check numerical stability properties when dG/d(u,p) is highly stiff

The implicit layers approach to calculating gradients requires solving a linear system with A::Matrix \ x::Vector where A is the Jacobian dG/d(u,p) where G = [ F, det(J) ]. Let's make a plot of the percentage error between finite difference and autodiff as the condition number for A is increased. @rveltz I use the same linear solvers as you, do you know what happens when your matrix J = dF/du is ill-conditioned?

symbolic complexity of analytical forms

Currently we are using Mathematica scripts to evaluate the determinant of jacobian, its curvature and the integration region velocity, then copying the code to Julia. More complex models yield symbolic complexity where it is no longer feasible to do so.

We would like an autodiff way - ideally using Zygote.jl of computing the following

kwargs in continuation cause illegal instruction

adding any kwarg into Cont.continuation - in the below example verbosity=0

function continuation( f, u₀,p₀ ; kwargs...)

	u₀, _, stable = Cont.newton( u -> f(u,p₀), u₀, Cont.NewtonPar(verbose=false) )
	branch, _, _ = Cont.continuation( f, u₀,p₀,

		ContinuationPar{eltype(u₀),AbstractLinearSolver,EigenSolver}(
			pMin=kwargs[:pMin],pMax=kwargs[:pMax],ds=kwargs[:ds],
			maxSteps=kwargs[:maxSteps]) ; verbosity=0
	)
	return Tracker.data.(u₀), unpack(branch)...
end

crashes julia when running main.jl with the following output

Unreachable reached at 0x7f64eea046ac

signal (4): Illegal instruction
in expression starting at /home/gszep/Documents/code/fold-inference/main.jl:14
#infer#21 at /home/gszep/Documents/code/fold-inference/inference.jl:15
unknown function (ip: 0x7f64eea046eb)
jl_fptr_trampoline at /buildworker/worker/package_linux64/build/src/gf.c:1842
jl_invoke at /buildworker/worker/package_linux64/build/src/gf.c:2348
#infer at ./none:0
unknown function (ip: 0x7f64eea044a1)
jl_fptr_trampoline at /buildworker/worker/package_linux64/build/src/gf.c:1842
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2197
do_call at /buildworker/worker/package_linux64/build/src/interpreter.c:323
eval_value at /buildworker/worker/package_linux64/build/src/interpreter.c:411
eval_stmt_value at /buildworker/worker/package_linux64/build/src/interpreter.c:362 [inlined]
eval_body at /buildworker/worker/package_linux64/build/src/interpreter.c:773
jl_interpret_toplevel_thunk_callback at /buildworker/worker/package_linux64/build/src/interpreter.c:885
unknown function (ip: 0xfffffffffffffffe)
unknown function (ip: 0x7f64e182ba7f)
unknown function (ip: 0xc)
jl_interpret_toplevel_thunk at /buildworker/worker/package_linux64/build/src/interpreter.c:894
jl_toplevel_eval_flex at /buildworker/worker/package_linux64/build/src/toplevel.c:764
jl_parse_eval_all at /buildworker/worker/package_linux64/build/src/ast.c:883
include_string at ./loading.jl:1008
include_string at /home/gszep/.julia/packages/CodeTools/xGemk/src/eval.jl:30
unknown function (ip: 0x7f64eea011f3)
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2197
#127 at /home/gszep/.julia/packages/Atom/X8fAI/src/eval.jl:94
withpath at /home/gszep/.julia/packages/CodeTools/xGemk/src/utils.jl:30
jl_invoke at /buildworker/worker/package_linux64/build/src/gf.c:2332
withpath at /home/gszep/.julia/packages/Atom/X8fAI/src/eval.jl:47 [inlined]
#126 at /home/gszep/.julia/packages/Atom/X8fAI/src/eval.jl:93 [inlined]
with_logstate at ./logging.jl:395
with_logger at ./logging.jl:491 [inlined]
#125 at /home/gszep/.julia/packages/Atom/X8fAI/src/eval.jl:92 [inlined]
hideprompt at /home/gszep/.julia/packages/Atom/X8fAI/src/repl.jl:85
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2197
macro expansion at /home/gszep/.julia/packages/Atom/X8fAI/src/eval.jl:91 [inlined]
macro expansion at /home/gszep/.julia/packages/Media/ItEPc/src/dynamic.jl:24 [inlined]
#124 at /home/gszep/.julia/packages/Atom/X8fAI/src/eval.jl:86
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2197
handlemsg at /home/gszep/.julia/packages/Atom/X8fAI/src/comm.jl:164
unknown function (ip: 0x7f650f29d7ec)
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2197
jl_apply at /buildworker/worker/package_linux64/build/src/julia.h:1571 [inlined]
jl_f__apply at /buildworker/worker/package_linux64/build/src/builtins.c:556
#19 at ./task.jl:259
unknown function (ip: 0x7f650f2e4ca4)
jl_apply_generic at /buildworker/worker/package_linux64/build/src/gf.c:2197
jl_apply at /buildworker/worker/package_linux64/build/src/julia.h:1571 [inlined]
start_task at /buildworker/worker/package_linux64/build/src/task.c:572
unknown function (ip: 0xffffffffffffffff)
Allocations: 389195905 (Pool: 389146779; Big: 49126); GC: 724

Julia has exited. Press Enter to start a new session.

hopf bifurcation targets

use complex terms in eigenvalues to encourage hopf bifurcations but not saddles/pitchforks

optimise two-state model to produce pitchfork and saddle-node

we would like to test a model that has the ability to reproduce multiple bifurcation types and plot a dimensionally reduced parameter regions that reproduce each behaviour.

apply kde to target distribution

the hope is that smoothing out the target distribution so that values are continuous between 0 and 1 will smoothen the cost landscape

register package

narrative

start with double exclusive finished story - new is relay videos ****
main problem reminder : model bifurcation regions don't match flow cytometry data
previous proposal reminder: Gaussian processes pros/cons
justify move to psudedoarclengthcontinuation and autodiff methods

sampling of optimal parameter basins

this would help us determine the sloppy parameter directions as well as the equally valid hypothesis regions. Dimensionality reduced plots of these regions will help determine regions of qualitatively distinct behaviours.

bifurcation points pile up on same target location

currently the following exists as a local minimum in the cost function

we would like to add a regularisation term - possibly repulsive term between points - to get rid of this

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