Sampling transitions

Direct simulation

These functions generate noise-induced transitions between a given initial and final state via Monte Carlo rejection sampling. While transition samples one transition, the transitions function generates an ensemble of transition paths. It supports parallelization on multiple threads to speed up the run.

Missing docstring.

Missing docstring for transition. Check Documenter's build log for details.

CriticalTransitions.transitions — Function

transitions(
    sys::CoupledSDEs,
    x_i,
    x_f;
    ...
) -> CriticalTransitions.TransitionEnsemble{_A, _B, EnsembleSolution{T, N, S}} where {_A, _B, T, N, S}
transitions(
    sys::CoupledSDEs,
    x_i,
    x_f,
    N::Int64;
    radii,
    tmax,
    Nmax,
    cut_start,
    radius_directions,
    show_progress,
    EnsembleAlg,
    kwargs...
) -> CriticalTransitions.TransitionEnsemble{_A, _B, EnsembleSolution{T, N, S}} where {_A, _B, T, N, S}

Generates an ensemble of N transition samples of sys from point x_i to point x_f. The transitions is by default simulated using threading. To sample the transitions in serial, GPU or Distributed enverionment, pass the desired SciMLBase.EnsembleAlgorithm to the EnsembleAlg algorithm.

Keyword arguments

radii=(0.1, 0.1): radius of the ball around x_i and x_f, respectively
Nmax: number of attempts before the algorithm stops even if less than N transitions occurred.
tmax=1e3: maximum time when the simulation stops even x_f has not been reached
radius_directions=1:length(sys.u): the directions in phase space to consider when calculating the radii rad_i and rad_f. Defaults to all directions. To consider only a subspace of state space, insert a vector of indices of the dimensions to be included.
cut_start=true: if false, returns the whole trajectory up to the transition
show_progress=true: shows a progress bar with respect to Nmax
kwargs...: keyword arguments passed to CommonSolve.solve

See also transition.

Returns a TransitionEnsemble object.

source

Results from the transitions function are organized in the following types:

CriticalTransitions.TransitionEnsemble — Type

struct TransitionEnsemble{SSS, T, ES}

Ensemble of transition paths between two points in a state space.

Fields

paths::Vector: paths sampled from the transition process
times::Array{Vector{T}, 1} where T: coresponsing times of the paths
stats::CriticalTransitions.TransitionStatistics: statistics of the ensemble
sciml_ensemble::Any: original ensemble solution of the SciML Ensemble problem

Constructors

TransitionEnsemble(sim, success_rate)

defined at /home/runner/work/CriticalTransitions.jl/CriticalTransitions.jl/src/trajectories/TransitionEnsemble.jl:55.

source

CriticalTransitions.TransitionStatistics — Type

struct TransitionStatistics{T}

Statistics of the ensemble of transition paths between two points in a state space.

Fields

success_rate::Any: success rate of the transition process
residence_time::Any: mean residence time of the transition process
transition_time::Any: mean transition time of the transition process
rareness::Any: rareness of the transition process

Constructors

TransitionStatistics(sim, success_rate)

defined at /home/runner/work/CriticalTransitions.jl/CriticalTransitions.jl/src/trajectories/TransitionEnsemble.jl:23.

source

Pathspace sampling

System-independent implementation of pathspace sampling

We are planning to add a general implementation of pathspace sampling as described in Börner et al. (2024) (see article's Supplemental Material), where transition paths are sampled as stochastic bridges between a fixed start and end point in state space under stochastic gradient descent in pathspace.